MATLAB实现最速下降法_和牛顿法和共轭梯度法.docVIP

最速下降法： 题目：f x-2 ^2+ y-4 ^2 M文件： function [R,n] steel x0,y0,eps syms x; syms y; f x-2 ^2+ y-4 ^2; v [x,y]; j jacobian f,v ; T [subs j 1 ,x,x0 ,subs j 2 ,y,y0 ]; temp sqrt T 1 ^2+ T 2 ^2 ; x1 x0;y1 y0; n 0; syms kk; while temp eps d -T; f1 x1+kk*d 1 ;f2 y1+kk*d 2 ; fT [subs j 1 ,x,f1 ,subs j 2 ,y,f2 ]; fun sqrt fT 1 ^2+ fT 2 ^2 ; Mini Gold fun,0,1,0.00001 ; x0 x1+Mini*d 1 ;y0 y1+Mini*d 2 ; T [subs j 1 ,x,x0 ,subs j 2 ,y,y0 ]; temp sqrt T 1 ^2+ T 2 ^2 ; x1 x0;y1 y0; n n+1; end R [x0,y0] 调用黄金分割法： M文件： function Mini Gold f,a0,b0,eps syms x;format long; syms kk; u a0+0.382* b0-a0 ; v a0+0.618* b0-a0 ; k 0; a a0;b b0; array k+1,1 a;array k+1,2 b; while b-a / b0-a0 eps Fu subs f,kk,u ; Fv subs f,kk,v ; if Fu Fv b v; v u; u a+0.382* b-a ; k k+1; elseif Fu Fv a u; u v; v a+0.618* b-a ; k k+1; end array k+1,1 a;array k+1,2 b; end Mini a+b /2; 输入： [R,n] steel 0,1,0.0001 R 1.座机电话号码667642 3.座机电话号码501463 R 1.座机电话号码667642 3.座机电话号码501463 n 1 牛顿法： 题目：f x-2 ^2+ y-4 ^2 M文件： syms x1 x2; f x1-2 ^2+ x2-4 ^2； v [x1,x2]; df jacobian f,v ; df df.; G jacobian df,v ; epson 1e-12;x0 [0,0];g1 subs df, x1,x2 , x0 1,1 ,x0 2,1 ;G1 subs G, x1,x2 , x0 1,1 ,x0 2,1 ;k 0;mul_count 0;sum_count 0; mul_count mul_count+12;sum_count sum_count+6; while norm g1 epson p -G1\g1; x0 x0+p; g1 subs df, x1,x2 , x0 1,1 ,x0 2,1 ; G1 subs G, x1,x2 , x0 1,1 ,x0 2,1 ; k k+1; mul_count mul_count+16;sum_count sum_count+11; end; k x0 mul_count sum_count 结果：：k 1 x0 2 4 mul_count 28 sum_count 17 共轭梯度法：f x-2 ^2+ y-4 ^2 M文件： function f conjugate_grad_2d x0,t x x0; syms xi yi a f x-2 ^2+ yi-4 ^2; fx diff f,xi ; fy diff f,yi ; fx subs fx, xi,yi ,x0 ; fy subs fy, xi,yi ,x0 ; fi [fx,fy]; count 0; while double sqrt fx^2+fy^2 t s -fi; if count 0 s -fi; else s s1; end x x+a*s; f subs f, xi,yi ,x ; f1 diff f ; f1 solve f1 ; if f1~ 0 ai double f1 ; else break x,f subs f, xi,yi ,x ,count end x subs x,a,ai ; f xi-xi^2+2*xi*yi+yi^2; fxi diff f,xi ; fyi diff f,yi ; fxi subs fxi, x