10个重要的算法C语言实现源代码(其4和5---龙贝格和牛顿迭代)

4.龙贝格求积公式，求解定积分#include<stdio.h> #include<math.h>#define f(x) (sin(x)/x)#define N20#define MAX20#define a2#define b4#define e0.00001float LBG(float p,float q,int n){int i;float sum=0,h=(q-p)/n;for (i=1;i<n;i++)sum+=f(p+i*h);sum+=(f(p)+f(q))/2;return(h*sum);}void main(){int i;int n=N,m=0;float T[MAX+1][2];T[0][1]=LBG(a,b,n);n*=2;for(m=1;m<MAX;m++){for(i=0;i<m;i++)T[i][0]=T[i][1];T[0][1]=LBG(a,b,n);n*=2;for(i=1;i<=m;i++)T[i][1]=T[i-1][1]+(T[i-1][1]-T[i-1][0])/(pow(2,2*m)-1);if((T[m-1][1]<T[m][1]+e)&&(T[m-1][1]>T[m][1]-e)){ printf("Answer=%f/n",T[m][1]); getch();return ;}}}

5.牛顿迭代公式，求方程的近似解

#include<stdio.h>#include<math.h>#include<conio.h>#define N 100#define PS 1e-5#define TA 1e-5float Newton(float (*f)(float),float(*f1)(float),float x0 ){ float x1,d=0;int k=0;do{ x1= x0-f(x0)/f1(x0);if((k++>N)||(fabs(f1(x1))<PS)){ printf("/nFailed!");getch();exit();}d=(fabs(x1)<1?x1-x0:(x1-x0)/x1);x0=x1;printf("x(%d)=%f/n",k,x0);}while((fabs(d))>PS&&fabs(f(x1))>TA) ;return x1;}float f(float x){ return x*x*x+x*x-3*x-3; }float f1(float x){ return 3.0*x*x+2*x-3; }void main(){ float f(float);float f1(float);float x0,y0;printf("Input x0: ");scanf("%f",&x0);printf("x(0)=%f/n",x0);y0=Newton(f,f1,x0);printf("/nThe root is x=%f/n",y0);getch();}