mulnumyt.m

非线性方程求解1--5（4） 非线性方程求解1--5（4）

function [r,m]=mulNumYT(F,x0,h,N,eps)
format long;
if nargin==4
    eps=1.0e-8;
end

n = length(x0);
fx0 = subs(F,findsym(F),x0);
x0 = transpose(x0);
J = zeros(n,n);
for k=0:N-1
    fx = subs(F,findsym(F),x0);
    for i=1:n
        x1 = x0;
        x1(i) = x1(i)+h(i);
        J(:,i) = (subs(F,findsym(F),x1)-fx)/h(i);
    end
    inJ = inv(J);
    r=x0-inJ*(fx-(1-k/N)*fx0);
    x0 = r;
end

m=1;
tol=1;
while tol>eps
    xs=r;
    fx = subs(F,findsym(F),xs);
    J = zeros(n,n);
    for i=1:n
        x1 = xs;
        x1(i) = x1(i)+h(i);
        J(:,i) = (subs(F,findsym(F),x1)-fx)/h(i);
    end
    r=xs-inv(J)*fx;                               %核心迭代公式
    tol=norm(r-xs);
    m=m+1;
    if(m>100000)                                              %迭代步数控制
        disp('迭代步数太多，可能不收敛！');
        return;
    end
end
format short;