6. 牛顿-科特斯求积公式，求定积分
- C/C++ code
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#include<stdio.h>#include<math.h>int NC(a,h,n,r,f)float (*a)[];float h;int n,f;float *r;{ int nn,i; float ds; if(n>1000||n<2) { if (f) printf("/n Faild! Check if 1<n<1000!/n",n); return(-1);}if(n==2){ *r=0.5*((*a)[0]+(*a)[1])*(h);return(0);}if (n-4==0) { *r=0;*r=*r+0.375*(h)*((*a)[n-4]+3*(*a)[n-3]+3*(*a)[n-2]+(*a)[n-1]);return(0);}if(n/2-(n-1)/2<=0)nn=n;elsenn=n-3;ds=(*a)[0]-(*a)[nn-1];for(i=2;i<=nn;i=i+2)ds=ds+4*(*a)[i-1]+2*(*a)[i];*r=ds*(h)/3;if(n>nn)*r=*r+0.375*(h)*((*a)[n-4]+3*(*a)[n-3]+3*(*a)[n-2]+(*a)[n-1]);return(0);}main(){ float h,r; int n,ntf,f; int i; float a[16];printf("Input the x[i](16):/n"); for(i=0;i<=15;i++) scanf("%d",&a[i]);h=0.2;f=0;ntf=NC(a,h,n,&r,f);if(ntf==0) printf("/nR=%f/n",r); else printf("/n Wrong!Return code=%d/n",ntf); getch();}
7.雅克比迭代，求解方程近似解
- C/C++ code
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#include <stdio.h>#include <math.h>#define N 20#define MAX 100#define e 0.00001int main(){ int n; int i,j,k; float t; float a[N][N],b[N][N],c[N],g[N],x[N],h[N]; printf("/nInput dim of n:"); scanf("%d",&n); if(n>N) { printf("Faild! Check if 0<n<N!/n"); getch(); return 1; } if(n<=0) {printf("Faild! Check if 0<n<N!/n"); getch(); return 1;} printf("Input a[i,j],i,j=0…%d:/n",n-1); for(i=0;i<n;i++) for(j=0;j<n;j++) scanf("%f",&a[i][j]); printf("Input c[i],i=0…%d:/n",n-1); for(i=0;i<n;i++)scanf("%f",&c[i]); for(i=0;i<n;i++) for(j=0;j<n;j++) { b[i][j]=-a[i][j]/a[i][i]; g[i]=c[i]/a[i][i]; } for(i=0;i<MAX;i++) { for(j=0;j<n;j++) h[j]=g[j]; { for(k=0;k<n;k++) { if(j==k) continue; h[j]+=b[j][k]*x[k]; } } t=0; for(j=0;j<n;j++) if(t<fabs(h[j]-x[j])) t=fabs(h[j]-x[j]); for(j=0;j<n;j++) x[j]=h[j]; if(t<e) { printf("x_i=/n"); for(i=0;i<n;i++) printf("x[%d]=%f/n",i,x[i]); getch(); return 0; } printf("after %d repeat , return/n",MAX); getch(); return 1; } getch();}
8.秦九昭算法
- C/C++ code
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#include <math.h>float qin(float a[],int n,float x){ float r=0; int i; for(i=n;i>=0;i--) r=r*x+a[i]; return r;}main(){ float a[50],x,r=0; int n,i; do { printf("Input frequency:"); scanf("%d",&n); } while(n<1); printf("Input value:"); for(i=0;i<=n;i++) scanf("%f",&a[i]); printf("Input frequency:"); scanf("%f",&x); r=qin(a,n,x); printf("Answer:%f",r); getch();}
9.幂法
- C/C++ code
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#include<stdio.h>#include<math.h>#define N 100#define e 0.00001#define n 3float x[n]={0,0,1};float a[n][n]={{2,3,2},{10,3,4},{3,6,1}};float y[n];main(){ int i,j,k; float xm,oxm; oxm=0; for(k=0;k<N;k++) { for(j=0;j<n;j++) { y[j]=0; for(i=0;i<n;i++) y[j]+=a[j][i]*x[i]; } xm=0; for(j=0;j<n;j++) if(fabs(y[j])>xm) xm=fabs(y[j]); for(j=0;j<n;j++) y[j]/=xm; for(j=0;j<n;j++) x[j]=y[j]; if(fabs(xm-oxm)<e) { printf("max:%f/n/n",xm); printf("v[i]:/n"); for(k=0;k<n;k++) printf("%f/n",y[k]); break; } oxm=xm; } getch();}
10.高斯塞德尔
- C/C++ code
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#include<math.h>#include<stdio.h>#define N 20#define M 99float a[N][N];float b[N];int main(){ int i,j,k,n; float sum,no,d,s,x[N]; printf("/nInput dim of n:"); scanf("%d",&n); if(n>N) { printf("Faild! Check if 0<n<N!/n "); getch(); return 1; } if(n<=0) { printf("Faild! Check if 0<n<N!/n ");getch();return 1;} printf("Input a[i,j],i,j=0…%d:/n",n-1); for(i=0;i<n;i++) for(j=0;j<n;j++) scanf("%f",&a[i][j]); printf("Input b[i],i=0…%d:/n",n-1); for(i=0;i<n;i++) scanf("%f",&b[i]); for(i=0;i<n;i++) x[i]=0; k=0; printf("/nk=%dx=",k); for(i=0;i<n;i++) printf("%12.8f",x[i]); do { k++; if(k>M){printf("/nError!/n”);getch();} break; } no=0.0; for(i=0;i<n;i++) { s=x[i]; sum=0.0; for(j=0;j<n;j++) if (j!=i) sum=sum+a[i][j]*x[j]; x[i]=(b[i]-sum)/a[i][i]; d=fabs(x[i]-s); if (no<d) no=d; } printf("/nk=%2dx=",k); for(i=0;i<n;i++) printf("%f",x[i]);}while (no>=0.1e-6);if(no<0.1e-6){ printf("/n/n answer=/n"); printf("/nk=%d",k); for (i=0;i<n;i++) printf("/n x[%d]=%12.8f",i,x[i]);}getch();}
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