VOLUME 85
NUMBER 302
A M E R I C A N
NOVEMBER 2016
M A T H E M A T I C A L
S O C I E T Y
EDITED BY
Remi Abgrall
Daniele Boffi
Martin Burger
Susanne C. Brenner, Managing Editor
Zhiming Chen
Albert Cohen
Ronald F. A. Cools
Qiang Du
Vivette Girault
Nicholas I. M. Gould
Ivan Graham
Gregor Kemper
Frances Kuo
Stig Larsson
Christian Lubich
Gunter Malle
James McKee
Michael J. Mossinghoff
Adam M. Oberman
Cheryl E. Praeger
Christoph Schwab
Zuowei Shen
Igor E. Shparlinski
Chi-Wang Shu
Andrew V. Sutherland
Daniel B. Szyld
Mark van Hoeij
Hans Volkmer
Barbara Wohlmuth
Zhimin Zhang
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MATHEMATICS OF COMPUTATION
CONTENTS
Vol. 85, No. 302
November 2016
Long Chen, Ricardo H. Nochetto, Enrique Otárola, and Abner J.
Salgado, Multilevel methods for nonuniformly elliptic operators and
fractional diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bernardo Cockburn and Alan Demlow, Hybridizable discontinuous
Galerkin and mixed finite element methods for elliptic problems on
surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mark Ainsworth, Johnny Guzmán, and Francisco-Javier Sayas,
Discrete extension operators for mixed finite element spaces on locally
refined meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Martin Campos Pinto and Eric Sonnendrücker, Gauss-compatible
Galerkin schemes for time-dependent Maxwell equations . . . . . . . . . . . . .
Zhiming Chen, Xueshuang Xiang, and Xiaohui Zhang, Convergence
of the PML method for elastic wave scattering problems . . . . . . . . . . . . .
Yanlai Chen, Bernardo Cockburn, and Bo Dong, Superconvergent
HDG methods for linear, stationary, third-order equations in one-space
dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jean-David Benamou, Francis Collino, and Jean-Marie Mirebeau,
Monotone and consistent discretization of the Monge-Ampère operator
C. Bauzet, J. Charrier, and T. Gallouët, Convergence of flux-splitting
finite volume schemes for hyperbolic scalar conservation laws with a
multiplicative stochastic perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Emmanuel Audusse, François Bouchut, Marie-Odile Bristeau,
and Jacques Sainte-Marie, Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system . . . . . . . . . . . .
M. Bebendorf, M. Bollhöfer, and M. Bratsch, On the spectral
equivalence of hierarchical matrix preconditioners for elliptic problems
Philippe Chartier, Florian Méhats, Mechthild Thalhammer,
and Yong Zhang, Improved error estimates for splitting methods
applied to highly-oscillatory nonlinear Schrödinger equations . . . . . . . . .
Daniel B. Szyld and Fei Xue, Preconditioned eigensolvers for large-scale
nonlinear Hermitian eigenproblems with variational characterizations.
I. Extreme eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jingrun Chen and Jianfeng Lu, Analysis of the divide-and-conquer
method for electronic structure calculations . . . . . . . . . . . . . . . . . . . . . . . . . .
N. Gould, C. Ortner, and D. Packwood, A dimer-type saddle search
algorithm with preconditioning and linesearch . . . . . . . . . . . . . . . . . . . . . . .
Cormac O’Sullivan, Zeros of the dilogarithm . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Kalle Leppälä, Explicit lower bounds for linear forms . . . . . . . . . . . . . . . . . . . .
David J. Platt, Numerical computations concerning the GRH . . . . . . . . . . .
Evelyne Hubert and George Labahn, Computation of invariants of finite
abelian groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Michaël Rao and Matthieu Rosenfeld, Avoidability of long k-abelian
repetitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2583
2609
2639
2651
2687
2715
2743
2777
2815
2839
2863
2887
2919
2939
2967
2995
3009
3029
3051
Vladica Andrejić and Milos Tatarevic, Searching for a counterexample
to Kurepa’s conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3061
INDEX TO VOLUME 85 (2016)
Abatzoglou, Alexander, Alice Silverberg, Andrew V. Sutherland, and Angela Wong. A framework
for deterministic primality proving using elliptic curves with complex multiplication, 1461
Adhikari, S. D., L. Boza, S. Eliahou, J. M. Marı́n, M. P. Revuelta, and M. I. Sanz. On the n-color
Rado number for the equation x1 + x2 + · · · + xk + c = xk+1 , 2047
Ainsworth, Mark, Johnny Guzmán, and Francisco-Javier Sayas. Discrete extension operators for
mixed finite element spaces on locally refined meshes, 2639
Akrivis, Georgios. Stability properties of implicit–explicit multistep methods for a class of nonlinear parabolic equations, 2217
Akrivis, Georgios, and Emmanuil Katsoprinakis. Backward difference formulae: New multipliers
and stability properties for parabolic equations, 2195
Amadori, Debora, and Laurent Gosse. Error estimates for well-balanced and time-split schemes
on a locally damped wave equation, 601
Andersson, Adam, and Stig Larsson. Weak convergence for a spatial approximation of the nonlinear stochastic heat equation, 1335
Andrejić, Vladica, and Milos Tatarevic. Searching for a counterexample to Kurepa’s conjecture,
3061
Anghel, Catalina V. The self-power map and collecting all residue classes, 379
Antonopoulos, D. C., and V. A. Dougalis. Error estimates for the standard Galerkin-finite element method for the shallow water equations, 1143
Aspenberg, Magnus. See Bilarev, Todor
Audusse, Emmanuel, François Bouchut, Marie-Odile Bristeau, and Jacques Sainte-Marie. Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system, 2815
Bai, Shi, Cyril Bouvier, Alexander Kruppa, and Paul Zimmermann. Better polynomials for
GNFS, 861
Bailey, D. H., and J. M. Borwein. Computation and structure of character polylogarithms with
applications to character Mordell–Tornheim–Witten sums, 295
Balakrishnan, Jennifer S., J. Steffen Müller, and William A. Stein. A p-adic analogue of the
conjecture of Birch and Swinnerton-Dyer for modular abelian varieties, 983
Banks, William D., and Igor E. Shparlinski. On Gauss sums and the evaluation of Stechkin’s
constant, 2569
Bartels, Sören. Projection-free approximation of geometrically constrained partial differential
equations, 1033
Bauzet, C., J. Charrier, and T. Gallouët. Convergence of flux-splitting finite volume schemes
for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation, 2777
Bebendorf, M., M. Bollhöfer, and M. Bratsch. On the spectral equivalence of hierarchical matrix
preconditioners for elliptic problems, 2839
Benamou, Jean-David, Francis Collino, and Jean-Marie Mirebeau. Monotone and consistent
discretization of the Monge-Ampère operator, 2743
Berthon, Christophe. See Desveaux, Vivien
Berthon, Christophe, and Christophe Chalons. A fully well-balanced, positive and entropy-satisfying
Godunov-type method for the shallow-water equations, 1281
Bertók, Csanád, and Lajos Hajdu. A Hasse-type principle for exponential Diophantine equations
and its applications, 849
Bertozzi, Andrea L. See Craig, Katy
Bilarev, Todor, Magnus Aspenberg, and Dierk Schleicher. On the speed of convergence of Newton’s method for complex polynomials, 693
Boito, P., Y. Eidelman, and L. Gemignani. Implicit QR for companion-like pencils, 1753
Bokanowski, Olivier, Yingda Cheng, and Chi-Wang Shu. Convergence of discontinuous Galerkin
schemes for front propagation with obstacles, 2131
Bollhöfer, M. See Bebendorf, M.
Borwein, J. M. See Bailey, D. H.
Bostan, Alin, Guillaume Chèze, Thomas Cluzeau, and Jacques-Arthur Weil. Efficient algorithms
for computing rational first integrals and Darboux polynomials of planar polynomial vector
fields, 1393
Bouchut, François. See Audusse, Emmanuel
Bouillard, Anne, Erwan Faou, and Maxime Zavidovique. Fast weak–KAM integrators for separable Hamiltonian systems, 85
INDEX TO VOLUME 85 (2016)
Bouvier, Cyril. See Bai, Shi
Boza, L. See Adhikari, S. D.
Bracciali, C. F., J. H. McCabe, T. E. Pérez, and A. Sri Ranga. A class of orthogonal functions
given by a three term recurrence formula, 1837
Bratsch, M. See Bebendorf, M.
Bristeau, Marie-Odile. See Audusse, Emmanuel
Bröker, Reinier, and Jeff Hoffstein. Fourier coefficients of sextic theta series, 1901
Bruinier, Jan Hendrik, Stephan Ehlen, and Eberhard Freitag. Lattices with many Borcherds
products, 1953
Bugaevskaya, A. N. See Korobov, V. I.
Bugariu, Ioan Florin, Sorin Micu, and Ionel Rovenţa. Approximation of the controls for the beam
equation with vanishing viscosity, 2259
Büthe, Jan. Estimating π(x) and related functions under partial RH assumptions, 2483
Calvo, Juan G. A BDDC algorithm with deluxe scaling for H(curl) in two dimensions with
irregular subdomains, 1085
Cancès, Clément, and Cindy Guichard. Convergence of a nonlinear entropy diminishing Control
Volume Finite Element scheme for solving anisotropic degenerate parabolic equations, 549
Cao, Waixiang, and Zhimin Zhang. Superconvergence of local discontinuous Galerkin methods
for one-dimensional linear parabolic equations, 63
Chalons, Christophe. See Berthon, Christophe
Charrier, J. See Bauzet, C.
Chartier, Philippe, Florian Méhats, Mechthild Thalhammer, and Yong Zhang. Improved error
estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations, 2863
Chen, Hao. Computing the Mazur and Swinnerton-Dyer critical subgroup of elliptic curves, 2499
Chen, Jingrun, and Jianfeng Lu. Analysis of the divide-and-conquer method for electronic structure calculations, 2919
Chen, Long, Ricardo H. Nochetto, Enrique Otárola, and Abner J. Salgado. Multilevel methods
for nonuniformly elliptic operators and fractional diffusion, 2583
Chen, Sheng, Jie Shen, and Li-Lian Wang. Generalized Jacobi functions and their applications
to fractional differential equations, 1603
Chen, Wenbin, Yuan Liu, Cheng Wang, and Steven M. Wise. Convergence analysis of a fully
discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation, 2231
Chen, William Y. C., Larry X. W. Wang, and Gary Y. B. Xie. Finite differences of the logarithm
of the partition function, 825
Chen, Yanlai, Bernardo Cockburn, and Bo Dong. Superconvergent HDG methods for linear,
stationary, third-order equations in one-space dimension, 2715
Chen, Zhiming, Xueshuang Xiang, and Xiaohui Zhang. Convergence of the PML method for
elastic wave scattering problems, 2687
Cheng, Yingda. See Bokanowski, Olivier
Chèze, Guillaume. See Bostan, Alin
Christiansen, Snorre H., and Francesca Rapetti. On high order finite element spaces of differential forms, 517
Cilleruelo, Javier, Florian Luca, and Amalia Pizarro-Madariaga. Carmichael numbers in the
sequence (2n k + 1)n≥1 , 357
Cluzeau, Thomas. See Bostan, Alin
Cockburn, Bernardo. See Chen, Yanlai
Cockburn, Bernardo, and Alan Demlow. Hybridizable discontinuous Galerkin and mixed finite
element methods for elliptic problems on surfaces, 2609
Cockburn, Bernardo, Ricardo H. Nochetto, and Wujun Zhang. Contraction property of adaptive
hybridizable discontinuous Galerkin methods, 1113
Collino, Francis. See Benamou, Jean-David
Coquel, Frédéric, Edwige Godlewski, Khalil Haddaoui, Claude Marmignon, and Florent Renac.
Choice of measure source terms in interface coupling for a model problem in gas dynamics,
2305
Craig, Katy, and Andrea L. Bertozzi. A blob method for the aggregation equation, 1681
Demanet, Laurent, and Xiangxiong Zhang. Eventual linear convergence of the Douglas-Rachford
iteration for basis pursuit, 209
INDEX TO VOLUME 85 (2016)
Demlow, Alan. See Cockburn, Bernardo
Desveaux, Vivien, Markus Zenk, Christophe Berthon, and Christian Klingenberg. Well-balanced
schemes to capture non-explicit steady states: Ripa model, 1571
Donatelli, Marco, Carlo Garoni, Carla Manni, Stefano Serra-Capizzano, and Hendrik Speleers.
Spectral analysis and spectral symbol of matrices in isogeometric collocation methods, 1639
Dong, Bo. See Chen, Yanlai
Dopico, Froilán M., Javier González, Daniel Kressner, and Valeria Simoncini. Projection methods
for large-scale T-Sylvester equations, 2427
Dougalis, V. A. See Antonopoulos, D. C.
Dusart, Pierre. Estimates of ψ, θ for large values of x without the Riemann hypothesis, 875
Egan, Judith, and Ian M. Wanless. Enumeration of MOLS of small order, 799
Ehlen, Stephan. See Bruinier, Jan Hendrik
Eidelman, Y. See Boito, P.
Eliahou, S. See Adhikari, S. D.
Ern, Alexandre, and Friedhelm Schieweck. Discontinuous Galerkin method in time combined
with a stabilized finite element method in space for linear first-order PDEs, 2099
Fan, Zhitao, Hui Ji, and Zuowei Shen. Dual Gramian analysis: Duality principle and unitary
extension principle, 239
Faou, Erwan. See Bouillard, Anne
Faustmann, Markus, Jens Markus Melenk, and Dirk Praetorius. Existence of H-matrix approximants to the inverses of BEM matrices: The simple-layer operator, 119
Freitag, Eberhard. See Bruinier, Jan Hendrik
Fromentin, Jean, and Florent Hivert. Exploring the tree of numerical semigroups, 2553
Gallouët, T. See Bauzet, C.
Gao, Shuhong, Frank Volny IV, and Mingsheng Wang. A new framework for computing Gröbner
bases, 449
Garoni, Carlo. See Donatelli, Marco
Gatica, Gabriel N., Ricardo Ruiz-Baier, and Giordano Tierra. A mixed finite element method
for Darcy’s equations with pressure dependent porosity, 1
Gavhi, Mpfareleni Rejoyce. See de Villiers, Johan
Gemignani, L. See Boito, P.
Gobet, Emmanuel, and Plamen Turkedjiev. Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions, 1359
Godlewski, Edwige. See Coquel, Frédéric
Goetz, Claus R., and Armin Iske. Approximate solutions of generalized Riemann problems for
nonlinear systems of hyperbolic conservation laws, 35
González, Javier. See Dopico, Froilán M.
Gosse, Laurent. See Amadori, Debora
Gould, N., C. Ortner, and D. Packwood. A dimer-type saddle search algorithm with preconditioning and linesearch, 2939
Gracia, J. L., and E. O’Riordan. Numerical approximation of solution derivatives of singularly
perturbed parabolic problems of convection-diffusion type, 581
Grenié, Loı̈c, and Giuseppe Molteni. Explicit versions of the prime ideal theorem for Dedekind
zeta functions under GRH, 889
. Zeros of Dedekind zeta functions under GRH, 1503
. Explicit smoothed prime ideals theorems under GRH, 1875
Guichard, Cindy. See Cancès, Clément
Guzmán, Johnny. See Ainsworth, Mark
Guzmán, Johnny, Manuel A. Sánchez, and Marcus Sarkis. On the accuracy of finite element
approximations to a class of interface problems, 2071
Haddaoui, Khalil. See Coquel, Frédéric
Hajdu, Lajos. See Bertók, Csanád
Hausen, Jürgen, Simon Keicher, and Antonio Laface. Computing Cox rings, 467
Hejda, Tomáš, and Edita Pelantová. Spectral properties of cubic complex Pisot units, 401
Hiary, Ghaith A. An alternative to Riemann-Siegel type formulas, 1017
. A deterministic algorithm for integer factorization, 2065
Hivert, Florent. See Fromentin, Jean
Hoang, N. S. On node distributions for interpolation and spectral methods, 667
INDEX TO VOLUME 85 (2016)
Hoffstein, Jeff. See Bröker, Reinier
Hu, Lili, Yao Li, and Yingjie Liu. A limiting strategy for the back and forth error compensation
and correction method for solving advection equations, 1263
Hubert, Evelyne, and George Labahn. Computation of invariants of finite abelian groups, 3029
Hungria, Allan, Jean-Philippe Lessard, and J. D. Mireles James. Rigorous numerics for analytic
solutions of differential equations: The radii polynomial approach, 1427
Iske, Armin. See Goetz, Claus R.
Jacobson, M. J., Jr. See Mosunov, A. S.
Jeon, Daeyeol. Families of elliptic curves over cyclic cubic number fields with prescribed torsion,
1485
Jespers, E., A. Kiefer, and Á. del Rı́o. Presentations of groups acting discontinuously on direct
products of hyperbolic spaces, 2515
Ji, Hui. See Fan, Zhitao
Katsoprinakis, Emmanuil. See Akrivis, Georgios
Keicher, Simon. See Hausen, Jürgen
Kestler, Sebastian, Kristina Steih, and Karsten Urban. An efficient space-time adaptive wavelet
Galerkin method for time-periodic parabolic partial differential equations, 1309
Kiefer, A. See Jespers, E.
Kleinjung, Thorsten. Quadratic sieving, 1861
Klingenberg, Christian. See Desveaux, Vivien
Korobov, V. I., and A. N. Bugaevskaya. Almost power sum systems, 717
Krejić, Nataša, and J. M. Martı́nez. Inexact Restoration approach for minimization with inexact
evaluation of the objective function, 1775
Kressner, Daniel. See Dopico, Froilán M.
Krumm, David. Computing points of bounded height in projective space over a number field, 423
Kruppa, Alexander. See Bai, Shi
Labahn, George. See Hubert, Evelyne
Laface, Antonio. See Hausen, Jürgen
Lairez, Pierre. Computing periods of rational integrals, 1719
Larsson, Stig. See Andersson, Adam
Lebowitz-Lockard, Noah, and Carl Pomerance. Generating random factored Gaussian integers,
easily, 503
Lecaros, Rodrigo, and Enrique Zuazua. Control of 2D scalar conservation laws in the presence
of shocks, 1183
Leppälä, Kalle. Explicit lower bounds for linear forms, 2995
Lercier, Reynald, Christophe Ritzenthaler, and Jeroen Sijsling. Explicit Galois obstruction and
descent for hyperelliptic curves with tamely cyclic reduced automorphism group, 2011
Lessard, Jean-Philippe. See Hungria, Allan
Li, Yao. See Hu, Lili
Liu, Ji, and Stephen J. Wright. An accelerated randomized Kaczmarz algorithm, 153
Liu, Yingjie. See Hu, Lili
Liu, Yuan. See Chen, Wenbin
Lu, Jianfeng. See Chen, Jingrun
Luca, Florian. See Cilleruelo, Javier
Manni, Carla. See Donatelli, Marco
Marı́n, J. M. See Adhikari, S. D.
Marmignon, Claude. See Coquel, Frédéric
Martı́nez, J. M. See Krejić, Nataša
McCabe, J. H. See Bracciali, C. F.
Méhats, Florian. See Chartier, Philippe
Melenk, Jens Markus. See Faustmann, Markus
Melman, A. On Pellet’s theorem for a class of lacunary polynomials, 707
Meng, Xiong, Chi-Wang Shu, and Boying Wu. Optimal error estimates for discontinuous Galerkin
methods based on upwind-biased fluxes for linear hyperbolic equations, 1225
Micu, Sorin. See Bugariu, Ioan Florin
Mirebeau, Jean-Marie. See Benamou, Jean-David
Mireles James, J. D. See Hungria, Allan
INDEX TO VOLUME 85 (2016)
Moeller, Michael, and Xiaoqun Zhang. Fast sparse reconstruction: Greedy inverse scale space
flows, 179
Molteni, Giuseppe. See Grenié, Loı̈c
Moody, Dustin, and Daniel Shumow. Analogues of Vélu’s formulas for isogenies on alternate
models of elliptic curves, 1929
Mosunov, A. S., and M. J. Jacobson, Jr. Unconditional class group tabulation of imaginary
quadratic fields to k∆k < 240 , 1983
Müller, J. Steffen. See Balakrishnan, Jennifer S.
Nakatsukasa, Yuji, and Vanni Noferini. On the stability of computing polynomial roots via confederate linearizations, 2391
Ngo, Hoang-Long, and Dai Taguchi. Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients, 1793
Nguyen, Hoi H. On a condition number of general random polynomial systems, 737
Nochetto, Ricardo H. See Chen, Long
. See Cockburn, Bernardo
Noferini, Vanni. See Nakatsukasa, Yuji
Olshanskii, Maxim A., and Danil Safin. A narrow-band unfitted finite element method for elliptic
PDEs posed on surfaces, 1549
O’Riordan, E. See Gracia, J. L.
Ortner, C. See Gould, N.
O’Sullivan, Cormac. Zeros of the dilogarithm, 2967
Otárola, Enrique. See Chen, Long
Packwood, D. See Gould, N.
Pelantová, Edita. See Hejda, Tomáš
Pérez, T. E. See Bracciali, C. F.
Pinto, Martin Campos, and Eric Sonnendrücker. Gauss-compatible Galerkin schemes for timedependent Maxwell equations, 2651
Pizarro-Madariaga, Amalia. See Cilleruelo, Javier
Platt, David J. Numerical computations concerning the GRH, 3009
Platt, D. J., and T. S. Trudgian. On the first sign change of θ(x) − x, 1539
Pomerance, Carl. See Lebowitz-Lockard, Noah
Praetorius, Dirk. See Faustmann, Markus
Qiu, Tianyu, and Francisco-Javier Sayas. The Costabel-Stephan system of boundary integral
equations in the time domain, 2341
Ramaré, O. An explicit density estimate for Dirichlet L-series, 325
Rao, Michaël, and Matthieu Rosenfeld. Avoidability of long k-abelian repetitions, 3051
Rapetti, Francesca. See Christiansen, Snorre H.
Raum, Martin. Computing genus 1 Jacobi forms, 931
Reddy, G. Murali Mohan, and Rajen K. Sinha. On the Crank-Nicolson anisotropic a posteriori
error analysis for parabolic integro-differential equations, 2365
Renac, Florent. See Coquel, Frédéric
Revuelta, M. P. See Adhikari, S. D.
del Rı́o, Á. See Jespers, E.
Ritzenthaler, Christophe. See Lercier, Reynald
Rivin, Igor. How to pick a random integer matrix? (and other questions), 783
Rosenfeld, Matthieu. See Rao, Michaël
Rovenţa, Ionel. See Bugariu, Ioan Florin
Ruiz-Baier, Ricardo. See Gatica, Gabriel N.
Ryan, Nathan C., and Gonzalo Tornarı́a, contributor Ralf Schmidt. Formulas for central values
of twisted spin L-functions attached to paramodular forms, 907
Safin, Danil. See Olshanskii, Maxim A.
Sainte-Marie, Jacques. See Audusse, Emmanuel
Salgado, Abner J. See Chen, Long
Sánchez, Manuel A. See Guzmán, Johnny
Sanz, M. I. See Adhikari, S. D.
Sarkis, Marcus. See Guzmán, Johnny
Sauer, Martin, and Wilhelm Stannat. Analysis and approximation of stochastic nerve axon equations, 2457
INDEX TO VOLUME 85 (2016)
Sayas, Francisco-Javier. See Ainsworth, Mark
. See Qiu, Tianyu
Schieweck, Friedhelm. See Ern, Alexandre
Schleicher, Dierk. See Bilarev, Todor
Schmidt, Ralf. See Ryan, Nathan C.
Schötzau, Dominik, Christoph Schwab, and Thomas P. Wihler. hp-dGFEM for second-order
mixed elliptic problems in polyhedra, 1051
Schwab, Christoph. See Schötzau, Dominik
Serra-Capizzano, Stefano. See Donatelli, Marco
Shen, Jie. See Chen, Sheng
Shen, Yun-Qiu, and Tjalling J. Ypma. Rank deficiencies and bifurcation into affine subspaces
for separable parameterized equations, 271
Shen, Zuowei. See Fan, Zhitao
Sheng Chang-tao. See Wang Zhong-qing
Shparlinski, Igor E. See Banks, William D.
Shu, Chi-Wang. See Bokanowski, Olivier
. See Meng, Xiong
Shumow, Daniel. See Moody, Dustin
Sijsling, Jeroen. See Lercier, Reynald
Silverberg, Alice. See Abatzoglou, Alexander
Simoncini, Valeria. See Dopico, Froilán M.
Sinha, Rajen K. See Reddy, G. Murali Mohan
Soga, Kohei. More on stochastic and variational approach to the Lax-Friedrichs scheme, 2161
Sonnendrücker, Eric. See Pinto, Martin Campos
Sørevik, Tor. Good low degree rank-1 lattice rules of high dimension, 1821
Speleers, Hendrik. See Donatelli, Marco
Sri Ranga, A. See Bracciali, C. F.
Stannat, Wilhelm. See Sauer, Martin
Steih, Kristina. See Kestler, Sebastian
Stein, William A. See Balakrishnan, Jennifer S.
Sutherland, Andrew V. See Abatzoglou, Alexander
Szyld, Daniel B., and Fei Xue. Preconditioned eigensolvers for large-scale nonlinear Hermitian
eigenproblems with variational characterizations. I. Extreme eigenvalues, 2887
Taguchi, Dai. See Ngo, Hoang-Long
Tatarevic, Milos. See Andrejić, Vladica
Thalhammer, Mechthild. See Chartier, Philippe
Tierra, Giordano. See Gatica, Gabriel N.
Tornarı́a, Gonzalo. See Ryan, Nathan C.
Trudgian, T. S. See Platt, D. J.
Tuitman, Jan. Counting points on curves using a map to P1 , 961
Turkedjiev, Plamen. See Gobet, Emmanuel
Urban, Karsten. See Kestler, Sebastian
de Villiers, Johan, and Mpfareleni Rejoyce Gavhi. Local interpolation with optimal polynomial
exactness in refinement spaces, 759
Volny, Frank, IV. See Gao, Shuhong
Wang, Cheng. See Chen, Wenbin
Wang, Larry X. W. See Chen, William Y. C.
Wang, Li-Lian. See Chen, Sheng
Wang, Mingsheng. See Gao, Shuhong
Wang Zhong-qing, and Sheng Chang-tao. An hp-spectral collocation method for nonlinear Volterra
integral equations with vanishing variable delays, 635
Wanless, Ian M. See Egan, Judith
Weil, Jacques-Arthur. See Bostan, Alin
Wihler, Thomas P. See Schötzau, Dominik
Wise, Steven M. See Chen, Wenbin
Wong, Angela. See Abatzoglou, Alexander
Wright, Stephen J. See Liu, Ji
Wu, Boying. See Meng, Xiong
INDEX TO VOLUME 85 (2016)
Xiang, Xueshuang. See Chen, Zhiming
Xie, Gary Y. B. See Chen, William Y. C.
Xu, Kejian. See Zhang, Long
Xue, Fei. See Szyld, Daniel B.
Ypma, Tjalling J. See Shen, Yun-Qiu
Zavidovique, Maxime. See Bouillard, Anne
Zenk, Markus. See Desveaux, Vivien
Zhang, Long, and Kejian Xu. The tame kernel of Q(ζ5 ) is trivial, 1523
Zhang, Wujun. See Cockburn, Bernardo
Zhang, Xiangxiong. See Demanet, Laurent
Zhang, Xiaohui. See Chen, Zhiming
Zhang, Xiaoqun. See Moeller, Michael
Zhang, Yong. See Chartier, Philippe
Zhang, Zhimin. See Cao, Waixiang
Zimmermann, Paul. See Bai, Shi
Zuazua, Enrique. See Lecaros, Rodrigo
VOLUME 85
A M E R I C A N
2016
M A T H E M A T I C A L
EDITED BY
Remi Abgrall
Daniele Boffi
Martin Burger
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Zhiming Chen
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Ivan Graham
Gregor Kemper
Frances Kuo
Stig Larsson
Christian Lubich
Gunter Malle
James McKee
Michael J. Mossinghoff
Adam M. Oberman
Cheryl E. Praeger
Christoph Schwab
Zuowei Shen
Igor E. Shparlinski
Chi-Wang Shu
Andrew V. Sutherland
Daniel B. Szyld
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Zhimin Zhang
PROVIDENCE, RHODE ISLAND USA
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MATHEMATICS OF COMPUTATION
CONTENTS
Vol. 85, No. 297
January 2016
Gabriel N. Gatica, Ricardo Ruiz-Baier, and Giordano Tierra, A
mixed finite element method for Darcy’s equations with pressure
dependent porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Claus R. Goetz and Armin Iske, Approximate solutions of generalized
Riemann problems for nonlinear systems of hyperbolic conservation laws
35
Waixiang Cao and Zhimin Zhang, Superconvergence of local discontinuous Galerkin methods for one-dimensional linear parabolic equations .
63
Anne Bouillard, Erwan Faou, and Maxime Zavidovique, Fast weak–
KAM integrators for separable Hamiltonian systems . . . . . . . . . . . . . . . . . .
85
Markus Faustmann, Jens Markus Melenk, and Dirk Praetorius,
Existence of H-matrix approximants to the inverses of BEM matrices:
The simple-layer operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Ji Liu and Stephen J. Wright, An accelerated randomized Kaczmarz
algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Michael Moeller and Xiaoqun Zhang, Fast sparse reconstruction: Greedy
inverse scale space flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Laurent Demanet and Xiangxiong Zhang, Eventual linear convergence
of the Douglas-Rachford iteration for basis pursuit . . . . . . . . . . . . . . . . . . . 209
Zhitao Fan, Hui Ji, and Zuowei Shen, Dual Gramian analysis: Duality
principle and unitary extension principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Yun-Qiu Shen and Tjalling J. Ypma, Rank deficiencies and bifurcation
into affine subspaces for separable parameterized equations . . . . . . . . . . . 271
D. H. Bailey and J. M. Borwein, Computation and structure of character
polylogarithms with applications to character Mordell–Tornheim–
Witten sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
O. Ramaré, An explicit density estimate for Dirichlet L-series . . . . . . . . . . . .
325
Javier Cilleruelo, Florian Luca, and Amalia Pizarro-Madariaga,
Carmichael numbers in the sequence (2n k + 1)n≥1 . . . . . . . . . . . . . . . . . . . . 357
Catalina V. Anghel, The self-power map and collecting all residue classes
379
Tomáš Hejda and Edita Pelantová, Spectral properties of cubic complex
Pisot units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
David Krumm, Computing points of bounded height in projective space over
a number field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
Shuhong Gao, Frank Volny IV, and Mingsheng Wang, A new
framework for computing Gröbner bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
Jürgen Hausen, Simon Keicher, and Antonio Laface, Computing Cox
rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
Noah Lebowitz-Lockard and Carl Pomerance, Generating random
factored Gaussian integers, easily . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
Vol. 85, No. 298
March 2016
Snorre H. Christiansen and Francesca Rapetti, On high order finite
element spaces of differential forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Clément Cancès and Cindy Guichard, Convergence of a nonlinear
entropy diminishing Control Volume Finite Element scheme for solving
anisotropic degenerate parabolic equations . . . . . . . . . . . . . . . . . . . . . . . . . . .
J. L. Gracia and E. O’Riordan, Numerical approximation of solution
derivatives of singularly perturbed parabolic problems of convectiondiffusion type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Debora Amadori and Laurent Gosse, Error estimates for well-balanced
and time-split schemes on a locally damped wave equation . . . . . . . . . . .
Wang Zhong-qing and Sheng Chang-tao, An hp-spectral collocation
method for nonlinear Volterra integral equations with vanishing variable
delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
N. S. Hoang, On node distributions for interpolation and spectral methods
Todor Bilarev, Magnus Aspenberg, and Dierk Schleicher, On the
speed of convergence of Newton’s method for complex polynomials . . .
A. Melman, On Pellet’s theorem for a class of lacunary polynomials . . . . . .
V. I. Korobov and A. N. Bugaevskaya, Almost power sum systems . . .
Hoi H. Nguyen, On a condition number of general random polynomial
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Johan de Villiers and Mpfareleni Rejoyce Gavhi, Local interpolation
with optimal polynomial exactness in refinement spaces . . . . . . . . . . . . . .
Igor Rivin, How to pick a random integer matrix? (and other questions) . .
Judith Egan and Ian M. Wanless, Enumeration of MOLS of small order
William Y. C. Chen, Larry X. W. Wang, and Gary Y. B. Xie, Finite
differences of the logarithm of the partition function . . . . . . . . . . . . . . . . . .
Csanád Bertók and Lajos Hajdu, A Hasse-type principle for exponential
Diophantine equations and its applications . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shi Bai, Cyril Bouvier, Alexander Kruppa, and Paul Zimmermann,
Better polynomials for GNFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pierre Dusart, Estimates of ψ, θ for large values of x without the Riemann
hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loı̈c Grenié and Giuseppe Molteni, Explicit versions of the prime ideal
theorem for Dedekind zeta functions under GRH . . . . . . . . . . . . . . . . . . . . .
Nathan C. Ryan and Gonzalo Tornarı́a, contributor Ralf Schmidt,
Formulas for central values of twisted spin L-functions attached to
paramodular forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Martin Raum, Computing genus 1 Jacobi forms . . . . . . . . . . . . . . . . . . . . . . . . .
Jan Tuitman, Counting points on curves using a map to P1 . . . . . . . . . . . . . .
Jennifer S. Balakrishnan, J. Steffen Müller, and William A. Stein,
A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for
modular abelian varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ghaith A. Hiary, An alternative to Riemann-Siegel type formulas . . . . . . .
517
549
581
601
635
667
693
707
717
737
759
783
799
825
849
861
875
889
907
931
961
983
1017
Vol. 85, No. 299
May 2016
Sören Bartels, Projection-free approximation of geometrically constrained
partial differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033
Dominik Schötzau, Christoph Schwab, and Thomas P. Wihler, hpdGFEM for second-order mixed elliptic problems in polyhedra . . . . . . . . 1051
Juan G. Calvo, A BDDC algorithm with deluxe scaling for H(curl) in two
dimensions with irregular subdomains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085
Bernardo Cockburn, Ricardo H. Nochetto, and Wujun Zhang,
Contraction property of adaptive hybridizable discontinuous Galerkin
methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113
D. C. Antonopoulos and V. A. Dougalis, Error estimates for the
standard Galerkin-finite element method for the shallow water equations 1143
Rodrigo Lecaros and Enrique Zuazua, Control of 2D scalar conservation
laws in the presence of shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1183
Xiong Meng, Chi-Wang Shu, and Boying Wu, Optimal error estimates
for discontinuous Galerkin methods based on upwind-biased fluxes for
linear hyperbolic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225
Lili Hu, Yao Li, and Yingjie Liu, A limiting strategy for the back and
forth error compensation and correction method for solving advection
equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1263
Christophe Berthon and Christophe Chalons, A fully well-balanced,
positive and entropy-satisfying Godunov-type method for the shallowwater equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1281
Sebastian Kestler, Kristina Steih, and Karsten Urban, An
efficient space-time adaptive wavelet Galerkin method for time-periodic
parabolic partial differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1309
Adam Andersson and Stig Larsson, Weak convergence for a spatial
approximation of the nonlinear stochastic heat equation . . . . . . . . . . . . . . 1335
Emmanuel Gobet and Plamen Turkedjiev, Linear regression MDP
scheme for discrete backward stochastic differential equations under
general conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1359
Alin Bostan, Guillaume Chèze, Thomas Cluzeau, and JacquesArthur Weil, Efficient algorithms for computing rational first integrals
and Darboux polynomials of planar polynomial vector fields . . . . . . . . . . 1393
Allan Hungria, Jean-Philippe Lessard, and J. D. Mireles James,
Rigorous numerics for analytic solutions of differential equations: The
radii polynomial approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1427
Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland,
and Angela Wong, A framework for deterministic primality proving
using elliptic curves with complex multiplication . . . . . . . . . . . . . . . . . . . . . 1461
Daeyeol Jeon, Families of elliptic curves over cyclic cubic number fields with
prescribed torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1485
Loı̈c Grenié and Giuseppe Molteni, Zeros of Dedekind zeta functions
under GRH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1503
Long Zhang and Kejian Xu, The tame kernel of Q(ζ5 ) is trivial . . . . . . . . 1523
D. J. Platt and T. S. Trudgian, On the first sign change of θ(x) − x . . . 1539
Vol. 85, No. 300
July 2016
Maxim A. Olshanskii and Danil Safin, A narrow-band unfitted finite
element method for elliptic PDEs posed on surfaces . . . . . . . . . . . . . . . . . .
Vivien Desveaux, Markus Zenk, Christophe Berthon, and Christian
Klingenberg, Well-balanced schemes to capture non-explicit steady
states: Ripa model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sheng Chen, Jie Shen, and Li-Lian Wang, Generalized Jacobi functions
and their applications to fractional differential equations . . . . . . . . . . . . .
Marco Donatelli, Carlo Garoni, Carla Manni, Stefano SerraCapizzano, and Hendrik Speleers, Spectral analysis and spectral
symbol of matrices in isogeometric collocation methods . . . . . . . . . . . . . . .
Katy Craig and Andrea L. Bertozzi, A blob method for the aggregation
equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pierre Lairez, Computing periods of rational integrals . . . . . . . . . . . . . . . . . . .
P. Boito, Y. Eidelman, and L. Gemignani, Implicit QR for companionlike pencils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nataša Krejić and J. M. Martı́nez, Inexact Restoration approach for
minimization with inexact evaluation of the objective function . . . . . . . .
Hoang-Long Ngo and Dai Taguchi, Strong rate of convergence for the
Euler-Maruyama approximation of stochastic differential equations with
irregular coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tor Sørevik, Good low degree rank-1 lattice rules of high dimension . . . . . .
C. F. Bracciali, J. H. McCabe, T. E. Pérez, and A. Sri Ranga, A class
of orthogonal functions given by a three term recurrence formula . . . . .
Thorsten Kleinjung, Quadratic sieving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loı̈c Grenié and Giuseppe Molteni, Explicit smoothed prime ideals
theorems under GRH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reinier Bröker and Jeff Hoffstein, Fourier coefficients of sextic theta
series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dustin Moody and Daniel Shumow, Analogues of Vélu’s formulas for
isogenies on alternate models of elliptic curves . . . . . . . . . . . . . . . . . . . . . . . .
Jan Hendrik Bruinier, Stephan Ehlen, and Eberhard Freitag,
Lattices with many Borcherds products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A. S. Mosunov and M. J. Jacobson, Jr., Unconditional class group
tabulation of imaginary quadratic fields to k∆k < 240 . . . . . . . . . . . . . . . .
Reynald Lercier, Christophe Ritzenthaler, and Jeroen Sijsling,
Explicit Galois obstruction and descent for hyperelliptic curves with
tamely cyclic reduced automorphism group . . . . . . . . . . . . . . . . . . . . . . . . . . .
1549
1571
1603
1639
1681
1719
1753
1775
1793
1821
1837
1861
1875
1901
1929
1953
1983
2011
S. D. Adhikari, L. Boza, S. Eliahou, J. M. Marı́n, M. P. Revuelta,
and M. I. Sanz, On the n-color Rado number for the equation
x1 + x2 + · · · + xk + c = xk+1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2047
Ghaith A. Hiary, A deterministic algorithm for integer factorization . . . . . 2065
Vol. 85, No. 301
September 2016
Johnny Guzmán, Manuel A. Sánchez, and Marcus Sarkis,
On the accuracy of finite element approximations to a class of interface
problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Alexandre Ern and Friedhelm Schieweck, Discontinuous Galerkin
method in time combined with a stabilized finite element method in
space for linear first-order PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Olivier Bokanowski, Yingda Cheng, and Chi-Wang Shu, Convergence
of discontinuous Galerkin schemes for front propagation with obstacles
Kohei Soga, More on stochastic and variational approach to the
Lax-Friedrichs scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Georgios Akrivis and Emmanuil Katsoprinakis, Backward difference
formulae: New multipliers and stability properties for parabolic
equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Georgios Akrivis, Stability properties of implicit–explicit multistep
methods for a class of nonlinear parabolic equations . . . . . . . . . . . . . . . . . .
Wenbin Chen, Yuan Liu, Cheng Wang, and Steven M. Wise,
Convergence analysis of a fully discrete finite difference scheme for the
Cahn-Hilliard-Hele-Shaw equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ioan Florin Bugariu, Sorin Micu, and Ionel Rovenţa, Approximation
of the controls for the beam equation with vanishing viscosity . . . . . . . .
Frédéric Coquel, Edwige Godlewski, Khalil Haddaoui, Claude
Marmignon, and Florent Renac, Choice of measure source terms
in interface coupling for a model problem in gas dynamics . . . . . . . . . . . .
Tianyu Qiu and Francisco-Javier Sayas, The Costabel-Stephan system of
boundary integral equations in the time domain . . . . . . . . . . . . . . . . . . . . . .
G. Murali Mohan Reddy and Rajen K. Sinha, On the Crank-Nicolson
anisotropic a posteriori error analysis for parabolic integro-differential
equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Yuji Nakatsukasa and Vanni Noferini, On the stability of computing
polynomial roots via confederate linearizations . . . . . . . . . . . . . . . . . . . . . . .
Froilán M. Dopico, Javier González, Daniel Kressner, and Valeria
Simoncini, Projection methods for large-scale T-Sylvester equations .
Martin Sauer and Wilhelm Stannat, Analysis and approximation of
stochastic nerve axon equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jan Büthe, Estimating π(x) and related functions under partial RH
assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hao Chen, Computing the Mazur and Swinnerton-Dyer critical subgroup of
elliptic curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2071
2099
2131
2161
2195
2217
2231
2259
2305
2341
2365
2391
2427
2457
2483
2499
E. Jespers, A. Kiefer, and Á. del Rı́o, Presentations of groups acting
discontinuously on direct products of hyperbolic spaces . . . . . . . . . . . . . . . 2515
Jean Fromentin and Florent Hivert, Exploring the tree of numerical
semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2553
William D. Banks and Igor E. Shparlinski, On Gauss sums and the
evaluation of Stechkin’s constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2569
Vol. 85, No. 302
November 2016
Long Chen, Ricardo H. Nochetto, Enrique Otárola, and Abner J.
Salgado, Multilevel methods for nonuniformly elliptic operators and
fractional diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bernardo Cockburn and Alan Demlow, Hybridizable discontinuous
Galerkin and mixed finite element methods for elliptic problems on
surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mark Ainsworth, Johnny Guzmán, and Francisco-Javier Sayas,
Discrete extension operators for mixed finite element spaces on locally
refined meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Martin Campos Pinto and Eric Sonnendrücker, Gauss-compatible
Galerkin schemes for time-dependent Maxwell equations . . . . . . . . . . . . . .
Zhiming Chen, Xueshuang Xiang, and Xiaohui Zhang, Convergence of
the PML method for elastic wave scattering problems . . . . . . . . . . . . . . . .
Yanlai Chen, Bernardo Cockburn, and Bo Dong, Superconvergent
HDG methods for linear, stationary, third-order equations in one-space
dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jean-David Benamou, Francis Collino, and Jean-Marie Mirebeau,
Monotone and consistent discretization of the Monge-Ampère operator
C. Bauzet, J. Charrier, and T. Gallouët, Convergence of flux-splitting
finite volume schemes for hyperbolic scalar conservation laws with a
multiplicative stochastic perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Emmanuel Audusse, François Bouchut, Marie-Odile Bristeau,
and Jacques Sainte-Marie, Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system . . . . . . . . . . . . .
M. Bebendorf, M. Bollhöfer, and M. Bratsch, On the spectral
equivalence of hierarchical matrix preconditioners for elliptic problems
Philippe Chartier, Florian Méhats, Mechthild Thalhammer,
and Yong Zhang, Improved error estimates for splitting methods
applied to highly-oscillatory nonlinear Schrödinger equations . . . . . . . . .
Daniel B. Szyld and Fei Xue, Preconditioned eigensolvers for large-scale
nonlinear Hermitian eigenproblems with variational characterizations. I.
Extreme eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jingrun Chen and Jianfeng Lu, Analysis of the divide-and-conquer
method for electronic structure calculations . . . . . . . . . . . . . . . . . . . . . . . . . .
N. Gould, C. Ortner, and D. Packwood, A dimer-type saddle search
algorithm with preconditioning and linesearch . . . . . . . . . . . . . . . . . . . . . . . .
2583
2609
2639
2651
2687
2715
2743
2777
2815
2839
2863
2887
2919
2939
Cormac O’Sullivan, Zeros of the dilogarithm . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Kalle Leppälä, Explicit lower bounds for linear forms . . . . . . . . . . . . . . . . . . . .
David J. Platt, Numerical computations concerning the GRH . . . . . . . . . . . .
Evelyne Hubert and George Labahn, Computation of invariants of finite
abelian groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Michaël Rao and Matthieu Rosenfeld, Avoidability of long k-abelian
repetitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vladica Andrejić and Milos Tatarevic, Searching for a counterexample to
Kurepa’s conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2967
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Editorial Committee
SUSANNE C. BRENNER, Chair, Center for Computation & Technology and Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803 USA;
E-mail: [email protected]
RONALD F. A. COOLS, Department of Computer Science, Katholieke Universiteit
Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium; E-mail: ronald.cools@cs.
kuleuven.ac.be
IGOR E. SHPARLINSKI, Department of Pure Mathematics, University of New South
Wales, Sydney, NSW 2052, Australia; E-mail: [email protected]
CHI-WANG SHU, Applied Mathematics Division, Brown University, P.O. Box F, 182
George St., Providence, RI 02912-0001 USA; E-mail: [email protected]
Board of Associate Editors
RÉMI ABGRALL, Institut für Mathematik, Universität Zürich, Winterthurerstrasse
190, CH-8057 Zürich, Switzerland; E-mail: [email protected]
DANIELE BOFFI, Department of Mathematics, University di Pavia, Via Ferrata 1,
27100 Pavia PV, Italy; E-mail: [email protected]
MARTIN BURGER, Institut für Numerische und Angewandte Mathematik, Westfaelisch Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany;
E-mail: [email protected]
ZHIMING CHEN, LSEC Institute of Computational Mathematics, Chinese Academy
of Sciences, Beijing 100190, China; E-mail: [email protected]
ALBERT COHEN, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie,
4, Place Jussieu, 75005 Paris, France; E-mail: [email protected]
QIANG DU, Columbia University, 500 W 120th Street, APAM, 200 Mudd, MC 4701,
New York, NY 10027, USA; E-mail:[email protected]
VIVETTE GIRAULT, Laboratoire Jacques-Louis Lions, Boite Courrier 187, Université de Pierre et Marie Curie, 4, place Jussieu, 75252 Paris Cedex 05, France; E-mail:
[email protected]
NICHOLAS I. M. GOULD, Department of Scientific Computing, G59, R18 STFCRutherford Appleton Laboratory, Chilton, Oxon OX11 0QX England; E-mail: nick.gould
@stfc.ac.uk
IVAN G. GRAHAM, Department of Mathematical Sciences, University of Bath, Bath
BA2 7AY, United Kingdom; E-mail: [email protected]
GREGOR KEMPER, Technische Universität München, Zentrum Mathematik M 11,
Boltzmannstr 3, 85748 Garching, Germany; E-mail: [email protected]
FRANCES KUO, University of New South Wales, School of Mathematics, Sydney
NSW 2052, Australia; E-mail: [email protected]
STIG LARSSON, Department of Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden; E-mail: [email protected]
CHRISTIAN LUBICH, Universität Tübingen, Mathematisches Institut, Auf der Morgenstelle 10, 72076 Tübingen, Germany; E-mail: [email protected]
GUNTER MALLE, Fachbereich Mathematik, Universität Kaiserslautern, Postfach 3049,
67653 Kaiserslautern, Germany; E-mail: [email protected]
JAMES MCKEE, Department of Mathematics, Royal Holloway University of London,
Egham Hill, Egham TW20 0EX, United Kingdom; E-mail: [email protected]
MICHAEL J. MOSSINGHOFF, Department of Mathematics, Davidson College, Box
6996, Davidson, NC 28035-6996 USA; E-mail: [email protected]
ADAM M. OBERMAN, McGill University, Department of Mathematics and Statistics,
805 Sherbrooke St W, Montreal QC H3A 0B9, Canada; E-mail: [email protected]
CHERYL E. PRAEGER, School of Mathematics and Statistics, M019, University of
Western Australia, 35 Stirling Highway, Crawley 6009, Western Australia, Australia;
E-mail: [email protected]
CHRISTOPH SCHWAB, ETH Zürich, Seminar for Applied Mathematics, Raemistrasse
101, HG G57.1, CH-8092 Zürich, Switzerland; E-mail: [email protected]
ZUOWEI SHEN, Department of Mathematics, National University of Singapore, Block
S17 10, Lower Kent Ridge Road, 119076 Singapore; E-mail: [email protected]
ANDREW V. SUTHERLAND, Department of Mathematics, Massachusetts Institute
of Technology, Cambridge, MA 02139 USA; E-mail: [email protected]
DANIEL B. SZYLD, Department of Mathematics 038-16, Temple University, 638
Wachman, 1805 N. Broad St. Philadelphia, PA 19122-6094 USA; E-mail: [email protected]
MARK van HOEIJ, Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL 32306 USA; E-mail: [email protected]
HANS VOLKMER, Department of Mathematical Sciences, University of WisconsinMilwaukee, P.O. Box 413, Milwaukee, WI 53201-0413 USA; E-mail: [email protected]
BARBARA WOHLMUTH, Fakultät für Mathematik, Technische Universität München,
Boltzmannstr. 3, 85748 Garching, Germany; E-mail: [email protected]
ZHIMIN ZHANG, Department of Mathematics, Wayne State University, Detroit, MI
48202 USA; E-mail: [email protected]
(Continued from back cover )
David J. Platt, Numerical computations concerning the GRH . . . . . . . . . . .
Evelyne Hubert and George Labahn, Computation of invariants of finite
abelian groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Michaël Rao and Matthieu Rosenfeld, Avoidability of long k-abelian
repetitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vladica Andrejić and Milos Tatarevic, Searching for a counterexample
to Kurepa’s conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3009
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CONTENTS
Vol. 85, No. 302
November 2016
NUMBER 302
PAGES 2583–3068
NOVEMBER 2016
0025-5718(201611)85:302*;1-6
VOLUME 85
Long Chen, Ricardo H. Nochetto, Enrique Otárola, and Abner J.
Salgado, Multilevel methods for nonuniformly elliptic operators and
fractional diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2583
Bernardo Cockburn and Alan Demlow, Hybridizable discontinuous
Galerkin and mixed finite element methods for elliptic problems on
surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2609
Mark Ainsworth, Johnny Guzmán, and Francisco-Javier Sayas,
Discrete extension operators for mixed finite element spaces on locally
refined meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2639
Martin Campos Pinto and Eric Sonnendrücker, Gauss-compatible
Galerkin schemes for time-dependent Maxwell equations . . . . . . . . . . . . . 2651
Zhiming Chen, Xueshuang Xiang, and Xiaohui Zhang, Convergence
of the PML method for elastic wave scattering problems . . . . . . . . . . . . . 2687
Yanlai Chen, Bernardo Cockburn, and Bo Dong, Superconvergent
HDG methods for linear, stationary, third-order equations in one-space
dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2715
Jean-David Benamou, Francis Collino, and Jean-Marie Mirebeau,
Monotone and consistent discretization of the Monge-Ampère operator 2743
C. Bauzet, J. Charrier, and T. Gallouët, Convergence of flux-splitting
finite volume schemes for hyperbolic scalar conservation laws with a
multiplicative stochastic perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2777
Emmanuel Audusse, François Bouchut, Marie-Odile Bristeau,
and Jacques Sainte-Marie, Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system . . . . . . . . . . . . 2815
M. Bebendorf, M. Bollhöfer, and M. Bratsch, On the spectral
equivalence of hierarchical matrix preconditioners for elliptic problems 2839
Philippe Chartier, Florian Méhats, Mechthild Thalhammer,
and Yong Zhang, Improved error estimates for splitting methods
applied to highly-oscillatory nonlinear Schrödinger equations . . . . . . . . . 2863
Daniel B. Szyld and Fei Xue, Preconditioned eigensolvers for large-scale
nonlinear Hermitian eigenproblems with variational characterizations.
I. Extreme eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2887
Jingrun Chen and Jianfeng Lu, Analysis of the divide-and-conquer
method for electronic structure calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 2919
N. Gould, C. Ortner, and D. Packwood, A dimer-type saddle search
algorithm with preconditioning and linesearch . . . . . . . . . . . . . . . . . . . . . . . 2939
Cormac O’Sullivan, Zeros of the dilogarithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2967
Kalle Leppälä, Explicit lower bounds for linear forms . . . . . . . . . . . . . . . . . . . . 2995
(Continued on inside back cover )
Mathematics of Computation
MATHEMATICS OF COMPUTATION