CH4非线性方程求根3埃特金算法正版

1、matlab1aitkenste?ensen?3.1.(aitken algorithm)21(aitkenalgorithm)xk +1= ?(xk),taylorxk +1-x?= ? ( )( xk- x?)(3.1)yk= xk +1= ? (xk),l ? ( ),yk- x?l(xk- x?)(3.2)zk= yk +1= ?(yk) = ? (?(xk),zk- x? l(yk- x?)(3.3)l3yk- x?yk-x?(yk- x?)2(xk- x?)( zk- x?)?y2k- 2ykx?xkzk- xkx?- zkx?(xk+ zk- 2yk)x? xkzk- y2k?x

2、?xkzk- y2kxk+ zk- 2yk?x?xk-(xk- yk)2x?xk?(?(xk) - (?(xk)2xk+ ?(? (xk) - 2?(xk)(3.5)x?5xk= ?(xk) -xk,2xk= xk+ ?(?(xk) - 2?(xk)(3.6)x?xk-(xk)21yk- x?l (xk- x?) ?x?yk- lxk1 -l+- l?3.2.(ste?ensen iteration)2(ste?ensen iteration)x? (x) = x -(x - ?(x)2x + ? (?(x) - 2? (x)(3.10)8xk+1= (xk) = xk-(xk- ? (xk)

3、2xk+ ? (?(xk) -2?(xk)(3.11)(ste?ensen iteration).92 (x) = ? (x) - x(3.12)x?yk= ? (xk),zk= yk +1= ? (yk) = ?(?(xk)(3.13) (xk) = ?(xk) - xk= yk- xk, (yk) = ?(yk) - yk= zk- yk(3.14)100: = (x)p (xk, (xk)q(yk, (yk)lk: = (xk) + (yk) - (xk)0 = (xk) + (yk) - (xk) (yk) - (xk) (xk)?xk +1xk-(yk-xk)2zk- 2yk+ xk

4、(3.17)121(ste?ensen iteration) (x) = x -(x - ?(x)2x + ? (?(x) - 2? (x)x? (x)?(x)x?(x)?(x?) = 1, (x)131? (x) = 1x?(x) - x = 0?(x) (x)isaacson e and h.b.keller. analysis of numericalmethods,new york,1966.142?(p+1)(x)p = 1,? (x) = 1ste?ensenp 1,xk +1= ?(xk)pste?ensen2p - 1p 1ste?ensenp = 1ste?ensen().15?3.3.1. ste?ensenf (x) = x3- x - 1 = 0, x0= 1.5ste?ensenxk +1= x3k-1 (x)16ste?ensen (x) = x -(x - ? (x)2(x3-1)3-1 + x - 2(x3-1)17x1= (x0) = x0-(x0- ?(x0)2(x30-1)3-1 + x0- 2(x30-1)= 1.5 -(1.53- 1.5 - 1)212.3965 + 1.5 - 2 2.37500= 1.5 -(0.875)29.1465= 1.5 -