最优化 二分法,Newton法,黄金分割法.doc

二分法和newton法： x2-2*x-1 syms x f=x2-2*x-1; subplot(1,2,1) m,n=erff(f,2,4,20,0.0001)m = 2.4142n = 14 subplot(1,2,2) o,p=newton(f,4,20,0.0001)o = 2.4142p = 5二分法函数：function root,n=erff(f,a,b,N,eps)k=0;f1=subs(f,findsym(sym(f),a);f2=subs(f,findsym(sym(f),b);if(f1=0) root=a; n=k; return;endif(f2=0) root=b; n=k; return;endif(f1*f20) disp(两端点点对应的函数值同号); return;endwhile(1) k=k+1; r=subs(f,findsym(sym(f),(a+b)/2); u(k)=abs(r); if(r=0) root=(a+b)/2; n=k; return; end if(f1*r0) b=(a+b)/2; end if(f2*r0) a=(a+b)/2; end if(abs(r)N) disp(迭代N次不出结果); return; endendnewton迭代法函数：function root n=newton(f,x0,N,eps)k=0;df=diff(f);if(subs(f,findsym(sym(f),x0)=0) root=x0; n=k; return;endwhile(1) k=k+1; x1=x0-subs(f,findsym(sym(f),x0)/subs(df,findsym(sym(f),x0); u(k)=abs(x1-x0); if(abs(x1-x0)N) disp(不收敛); return; endend黄金分割法： x2-sin(x) syms x phi=x2-sin(x); s,phis,k,G,E=golds(phi,0,1,1e-4,1e-5)s = 0.4502phis = -0.2325k = 21G = 0 0.3820 0.6180 1.0000 0 0.2361 0.3820 0.6180 0.2361 0.3820 0.4721 0.6180 0.3820 0.4721 0.5279 0.6180 0.3820 0.4377 0.4721 0.5279 0.3820 0.4164 0.4377 0.4721 0.4164 0.4377 0.4508 0.4721 0.4377 0.4508 0.4590 0.4721 0.4377 0.4458 0.4508 0.4590 0.4458 0.4508 0.4540 0.4590 0.4458 0.4489 0.4508 0.4540 0.4489 0.4508 0.4520 0.4540 0.4489 0.4501 0.4508 0.4520 0.4489 0.4497 0.4501 0.4508 0.4497 0.4501 0.4504 0.4508 0.4497 0.4499 0.4501 0.4504 0.4499 0.4501 0.4502 0.4504 0.4501 0.4502 0.4503 0.4504 0.4501 0.4502 0.4502 0.4503 0.4501 0.4502 0.4502 0.4502 0.4502 0.4502 0.4502 0.4502E = 1.0e-004 *0.6611 0.0000黄金分割法函数：function s,phis,k,G,E=golds(phi,a,b,delta,epsilon)t=(sqrt(5)-1)/2;h=b-a;phia=subs(phi,findsym(sym(phi),a);phib=subs(phi,findsym(sym(phi),b);p=a+(1-t)*h;q=a+t*h;phip=subs(phi,findsym(sym(phi),p);phiq=subs(phi,findsym(sym(phi),q);k=1;G(k,1:4)=a,p,q,b;while(abs(phib-phia)epsilon)|(hdelta) if(phipphiq) b=q; phib=phiq; q=p; phiq=phip; h=b-a; p=a+(1-t)*h; phip=subs(phi,findsym(sym(phi),p); else a=p; phia=phip; p=q; phip=phiq; h=b-a; q=a+t*h; phiq=subs(phi,findsym(sym(phi),q); end k=k+1; G(k,1:4)=