黃金分割法、二次插值法C語言編程

1、.已知：F(x)=x4-4x3-6x2-16x+4,求極小值，極小值點，區(qū)間，迭代次數(shù)？用進退法確定區(qū)間，用黃金分割法求極值。#include#include#definee0.001#definett0.01floatf(doublex)floaty=pow(x,4)-4*pow(x,3)-6*pow(x,2)-16*x+4;return(y);finding(float*p1,float*p2)floatx1=0,x2,x3,t,f1,f2,f3,h=tt;intn=0;x2=x1+h;f1=f(x1);f2=f(x2);if(f2f1)h=-h;t=x2;x2=x1;x1=t;dox3=

2、x2+h;h=2*h;f3=f(x3);n=n+1;while(f3x3)t=x1;x1=x3;x3=t;*p1=x1;*p2=x3;return(n);gold(float*p)floata,b,x1,x2,f1,f2;intn=0;finding(&a,&b);dox1=a+0.382*(b-a);x2=a+0.618*(b-a);f1=f(x1);f2=f(x2);n=n+1; if(f1f2)a=x1; elseb=x2;while(b-a)e);*p=(x1+x2)/2;return(n);main()floata,b,x,min;intn1,n2;n1=finding(&a,&b)

3、;n2=gold(&x);min=f(x);printf(nTheareais%fto%f.,a,b);printf(nThenunmber1is%d.,n1);printf(nTheminis%fandtheresultis%f.,x,min);printf(nThenunmber2is%d.,n2)二插法已知：F(x1,x2)=4*x1-x2的平方-12；求極小值，極小值點，迭代次數(shù)？用復(fù)合形法求極值。約束條件：x2=0;x1=0;25-x1的平方-x2的平方=0;#include#include#defineEP0.0001#defineE0.01#defineforifor(i=0;i

4、=1;i+)inti;floatf(float*p)floaty;y=4*p0-pow(p1,2)-12;return(y);intcons(float*q)intn;if(pow(q0,2)+pow(q1,2)-25=0)&(q1=0) n=1;else n=0;return(n);voidpaixu(float*p1,float*p2,float*p3)floatf1,f2,f3;floatL2,M2,H2;f1=f(p1);f2=f(p2);f3=f(p3);foriHi=p1i;Mi=p2i;Li=p3i;if(f1f2) if(f2f3)foriMi=p3i;Li=p2i; else

5、foriHi=p3i;Mi=p1i;Li=p2i;elseif(f2f3)foriHi=p2i;Mi=p1i;Li=p3i;elseforiHi=p2i;Mi=p3i;Li=p1i;forip1i=Hi;p2i=Mi;p3i=Li;floatr()float rr;dorr=rand();while(rr=0);rr=rr/32767;return(rr);main()floatx12=2,1,x22=4,1,x32=3,3;floatXC2,XR2,A2,B2;floatH=1.3,FH,FR,FC,FL,cha,min,S;inttf,tf1,tf2;do do paixu(x1,x2,x

6、3);/*foriprintf(nX1%dis%f,X2%dis%f,X3%dis%f.,i,x1i,i,x2i,i,x3i);*/foriXCi=(x2i+x3i)/2;/*foriprintf(nXC%dis%f.,i,XCi);*/tf1=cons(XC); if(tf1=0)FC=f(XC); FL=f(x3); if(FLFC)foriAi=x3i;Bi=XCi;elseforiAi=XCi;Bi=x3i;doS=r();x1i=Ai+S*(Bi-Ai);tf2=cons(x1);while(tf2=0);doS=r();x2i=Ai+S*(Bi-Ai);tf2=cons(x2);while(tf2=0);doS=r();x3i=Ai+S*(Bi-Ai);tf2=cons(x3);while(tf2=0); while(tf1=0);foriXRi=XCi+H*(XCi-x1i);/*foriprintf(nXR%dis%f.,i,XRi);*/FH=f(x1);FR=f(XR);tf=cons(XR);if(tf&(FRFH)forix1i=XRi;/*printf(n1);*/el