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27/03/2015 - Şeker Yatırım

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Formüller
Neville Metodu:
Qi,j (x) =
(x − xi−j )Qi,j−1 (x) − (x − xi )Qi−1,j−1 (x)
xi − xi−j
Bölünmü³ Fark Metodu:
Pn (x) = f [x0 ] +
n
X
f [x0 , x1 , · · · , xk ](x − x0 )(x − x1 ) · · · (x − xk−1 )
k=1
leri Fark Metodu:
n X
s
Pn (x) = f (x0 ) +
∆k f (x0 )
k
k=1
Merkezi Fark Metodu:
Pn (x) =P2m+1 (x) = f (x0 ) +
sh
(f [x−1 , x0 ] + f [x0 , x1 ]) + s2 h2 f [x−1 , x0 , x1 ]
2
s(s2 − 1)h3
(f [x−2 , x−1 , x0 , x1 ] + f [x−1 , x0 , x1 , x2 ])
2
+ · · · + s2 (s2 − 1)(s2 − 4) · · · (s2 − (m − 1)2 )h2m f [x−m , · · · , xm ]
s(s2 − 1) · · · (s2 − m2 )h2m+1
+
(f [x−m−1 , . . . , xm ] + f [x−m , · · · , xm+1 ])
2
+
Geri Fark Metodu:
Pn (x) = f (xn ) +
n
X
k=1
Fark Formülü:
f 0 (x0 ) =
(−1)
k
−s
∇k f (xn )
k
f (x0 + h) − f (x0 ) h 00
− f (ξ)
h
2
Üç-Nokta Uç Nokta Formülü:
f 0 (x0 ) =
h2
1
[−3f (x0 ) + 4f (x0 + h) − f (x0 + 2h)] + f 000 (ξ)
2h
3
Üç-Nokta Orta Nokta Formülü:
f 0 (x0 ) =
1
h2
[f (x0 + h) − f (x0 − h)] − f 000 (ξ)
2h
6
Be³-Nokta Orta Nokta Formülü:
f 0 (x0 ) =
1
h4
[f (x0 − 2h) − 8f (x0 − h) + 8f (x0 + h) − f (x0 + 2h)] + f (v) (ξ)
12h
30
Be³-Nokta Uç Nokta Formülü:
f 0 (x0 ) =
1
h4
[−25f (x0 ) + 48f (x0 + h) − 36f (x0 + 2h) + 16f (x0 + 3h) − 3f (x0 + 4h)] + f (v) (ξ)
12h
5
kinci Türev için Orta Nokta Formülü:
1
h2 (iv)
f (x0 ) = 2 [f (x0 − h) − 2f (x0 ) + f (x0 + h)] − f (ξ)
h
12
00
Richardson Ekstrapolasyon Formülü:
h
1
h
Nj (h) = Nj−1
+ j−1
Nj−1
− Nj−1 (h)
2
2 −1
2
1
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