非线性方程组数值方法
1非线性Seidel迭代求解非线性固定点方程组xGxfu
ctio
xiterseidelGxdeltamaxlI
putGisthe
o
li
earsystemsavedi
theMfileGmxisthei
itialguessatthesolutio
deltaistheerrorbou
dmaxlisthe
umberofiteratio
sOutputxistheseidelapproximatio
tothesolutio
iteristhe
umberofiteratio
srequired
le
gthxfork1maxlx0xx0isthekthapproximatio
tothesolutio
forj1
AfevalGx0Updatethetermsofx0astheyarecalculatedx0jAje
derrabs
ormx0xrelerrerr
ormx0epsxx0iterkiferrdeltarelerrdeltabreake
de
d
2牛顿拉夫申法求解非线性方程组Fx
0xk1xk
Fxkk012Fxk
fu
ctio
xitererr
ewto
dimFJFxdeltaepsilo
maxlI
putFisthe
o
li
earsystemsavedi
theMfileFmJFistheJacobia
ofFsavedastheMfileJFmxisthei
itialapproximatio
tothesolutio
deltaisthetolera
ceforxepsilo
isthetolera
ceforFxmaxlisthe
umberofiteratio
sOutputxistheseidelapproximatio
tothesolutio
iteristhe
umberofiteratio
srequirederristheerrorestimateforxyfevalFxfork1maxlJfevalJFxQxJyzfevalFQerr
ormQxrelerrerr
ormQepsxQyziterkiferrdeltarelerrdeltaabsyepsilo
breake
de
d例fu
ctio
zFXxX1yX2zzeros12
fz1x22xy05z2x24y24fu
ctio
wJFXxX1yX2w2x212x8yxitererr
ewto
dimFJF20250001000120
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