Newton.rar_newton_拟牛顿法_解非线性方程_非线性 牛顿_非线性方程

%Newton法解非性 clc tic; N=3 x0=[800,78,788]'; x=x0 for s=1:1:1000000 F=zeros(3,1); F(1)=3*x(1)-cos(x(2)*x(3))-1/2; F(2)=x(1)^2-81*(x(2)+0.1)^2+sin(x(3))+1.06; F(3)=exp(-x(2)*x(1))+20*x(3)+1/3*(10*pi-3); jacobi=[3,sin(x(2)*x(3)),sin(x(2)*x(3));... 2*x(1),-2*81*(x(2)+0.1),cos(x(3));... -x(2)*exp(-x(2)*x(1)),-x(1)*exp(-x(2)*x(1)),20]; x_n=x-jacobi^(-1)*F; if sum(abs(F))<0.000001 break end x=x_n; end s x F toc flops tic %拟牛顿法 x=x0; F1=zeros(3,1); jacobi=[3,sin(x(2)*x(3)),sin(x(2)*x(3));... 2*x(1),-2*81*(x(2)+0.1),cos(x(3));... -x(2)*exp(-x(2)*x(1)),-x(1)*exp(-x(2)*x(1)),20]; for s=1:1:1000000 F(1)=3*x(1)-cos(x(2)*x(3))-1/2; F(2)=x(1)^2-81*(x(2)+0.1)^2+sin(x(3))+1.06; F(3)=exp(-x(2)*x(1))+20*x(3)+1/3*(10*pi-3); x_n=x-jacobi^(-1)*F; if sum(abs(F))<0.000001 break end s=x_n-x; F1(1)=3*x_n(1)-cos(x_n(2)*x_n(3))-1/2; F1(2)=x_n(1)^2-81*(x_n(2)+0.1)^2+sin(x_n(3))+1.06; F1(3)=exp(-x_n(2)*x_n(1))+20*x_n(3)+1/3*(10*pi-3); y=F1-F; d_j=(y-jacobi*s)*(y-jacobi*s)'/((y-jacobi*s)'*s); jacobi=jacobi+d_j; x=x_n; end s x F toc