MATLAB语言常用算法程序集 非线性方程组求解.zip

function [r,m]=mulDamp(F,x0,h,u,v,eps) format long; if nargin==5 eps=1.0e-6; end FI = transpose(F)*F/2; n = length(x0); x0 = transpose(x0); m=1; tol=1; while tol>eps j = 0; fx = subs(F,findsym(F),x0); J = zeros(n,n); for i=1:n x1 = x0; x1(i) = x1(i)+h; afx = subs(F,findsym(F),x1); J(:,i) = (afx-fx)/h; end FIx = subs(FI,findsym(FI),x0); for i=1:n x2 = x0; x2(i) = x2(i)+h; gradFI(i,1) = (subs(FI,findsym(FI),x2)-FIx)/h; end s=0; while s==0 A = transpose(J)*J+u*eye(n,n); p = -A\gradFI; r = x0 + p; FIr = subs(FI,findsym(FI),r); if FIr<FIx if j == 0 u = u/v; j = 1; else s=1; end else u = u*v; j = 1; if norm(r-x0)<eps s=1; end end end x0 = r; tol = norm(p); 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;