用牛顿迭代法求解非线性方程组

用牛顿迭代法求解非线性方程组newton.m

clear

clc

[F,v]=wuzu;

x1=input('请输入初值:');

eps=input('请输入误差精度:');

b=jacobian(F,v);

for i=1:1:length(x1)

b=subs(b,v(i),x1(i));

F=subs(F,v(i),x1(i));

end

b=eval(b);

F=eval(F);

x2=x1-b\F';

i=1;

while max(abs(x2-x1))>=eps

x1=x2;

F=wuzu;

b=jacobian(F,v);

for i=1:1:length(x1)

b=subs(b,v(i),x1(i));

F=subs(F,v(i),x1(i));

end

b=eval(b);

F=eval(F);

x2=x1-b\F';

i=i+1;

if i==1000

break;

end

end

if i>=1000

disp('newton迭代法很可能不收敛!') else

disp('方程的根是：');

x=x2

End

wuzu.m

function [F,v]=wuzu syms x y

f1=x^2-10*x+y^2+8; f2=x*y^2+x-10*y+8; F=[f1,f2];

v=[x,y];

End