Newton-Raphson迭代

Question

x1和x2很复杂。示例：x1 = x1reel+x1img*i和x2 = x2reel-x2img*i。 x0是第一个价值和复杂的。

clc
clear all
% Define the given function
syms x1 x2

x=[x1,x2];

f(x)=[3*x1-cos(x1^2)-1/2;3*x2-cos(x2^2)-1/2];

% Define the stopping criteria based on Nither or relative errors

tol=10^-5; 
Niter=100;

df=jacobian(f,x);

x0=[complex;complex];

% Setting starting values

error=1; 
i=0; 

% Start the Newton-Raphson Iteration

while(abs(error)>tol)

f0=eval(f(x0(1),x0(2)));

df0=eval(df(x0(1),x0(2))); 

xnew=x0-df0\f0; % also tried lsqr(df0,f0),bicg(df0,f0)

error=norm(xnew-x0);

x0=xnew;

i=i+1

if i>=Niter

    fprintf('Iteration times spill over Niter\n');

    return;

end

end

我想做Newton-Raphson Iteration。但我很难，因为它很复杂。