最优化二分法,Newton法,黄金分割法

1、二分法和 newton 法：xA2-2*x-1>> syms x>> f=xA2-2*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=newto n(f,4,20,0.0001)o =2.4142p =5BJ Figure 1上丄邑1二分法函数：fun cti onroot, n=erff(f,a,b,N,eps)k=0;f1=subs(f,fi ndsym(sym(f),a);f2=subs(f

2、,fi ndsym(sym(f),b);if (f1=0)root=a;n=k;return ;endif (f2=0)root=b;n=k;return ;endif (f1*f2>0)disp( '两端点点对应的函数值同号 );return ;endwhile (1)k=k+1;r=subs(f,fi ndsym(sym(f),(a+b)/2);u(k)=abs(r);if (r=0)root=(a+b)/2;n=k;return ;endif (f1*r<0)b=(a+b)/2;endif (f2*r<0)a=(a+b)/2;endif (abs(r)<e

3、ps)root=(a+b)/2;n=k;plot(1:k,u(1:k),'r-');xlabel('迭代次数');ylabel('误差)；title('二分法');return ;endif (k>N)disp(迭代N次不岀结果);return ;endendnewton迭代法函数：fun cti onroot n=n ewt on( f,xO,N,eps)k=0;df=diff(f);if (subs(f,findsym(sym(f),xO)=O)root=x0;n=k;return ;endwhile (1)k=k+1;x1=x

4、0-subs(f,fi ndsym(sym(f),xO)/subs(df,fi ndsym(sym(f),xO); u(k)=abs(x1-x0);if (abs(x1-x0)<eps)root=x1;n=k;plot(1:k,u(1:k),'r');xlabel('迭代次数');ylabel('误差)；title('newton法');return ;endx0=x1;if (k>N)disp('不收敛');returnend end黄金分割法：xA2-s in(x)>> syms x>&g

5、t; phi=xA2-si n( x);>> s,phis,k,G ,E=golds(phi,0,1,1e-4,1e-5) s =0.4502phis =-0.2325k =21G =00.38200.61801.000000.23610.38200.61800.23610.38200.47210.61800.38200.47210.52790.61800.38200.43770.47210.52790.38200.41640.43770.47210.41640.43770.45080.47210.43770.45080.45900.47210.43770.44580.45080.

6、45900.44580.45080.45400.45900.44580.44890.45080.45400.44890.45080.45200.45400.44890.45010.45080.45200.44890.44970.45010.45080.44970.45010.45040.45080.44970.44990.45010.45040.44990.45010.45020.45040.45010.45020.45030.45040.45010.45020.45020.45030.45010.45020.45020.45020.45020.45020.45020.4502E =1.0e-

7、004 *0.6611 0.0000黄金分割法函数：fun cti ons,phis,k,G,E=golds(phi,a,b,delta,epsil on)t=(sqrt(5)-1)/2;h=b-a;phia=subs(phi,fi ndsym(sym(phi),a);phib=subs(phi,fi ndsym(sym(phi),b) p=a+(1_t)*h;q=a+t*h;phip=subs(phi,fi ndsym(sym(phi),p);phiq=subs(phi,fi ndsym(sym(phi),q) k=1;G(k,1:4)=a,p,q,b;while(abs(phib-phia)>epsil on )|(h>delta)if (phip<phiq)b=q; phib=phiq; q=p; phiq=phip;h=b-a; p=a+(1-t)*h; phip=subs(phi,fi ndsym(sym(phi),p);elsea=p; phia=phip; p=q; phip=phiq;h=b-a; q=a+t*h; phiq=subs(phi,fi ndsym(sym(phi),q);endk=k