10个重要的算法C语言实现源代码：拉格朗日，牛顿插值，高斯，龙贝格，牛顿迭代，牛顿-科特斯，雅克比，秦九昭，幂法，高斯塞德尔解决方法

#include <stdio.h>
 #include <conio.h>
 #include <alloc.h>
 float lagrange(float *x,float *y,float xx,int n)     /*拉格朗日插值算法*/
 { int i,j;
   float *a,yy=0.0;    /*a作为临时变量，记录拉格朗日插值多项式*/
   a=(float *)malloc(n*sizeof(float));
   for(i=0;i<=n-1;i++)
   { a[i]=y[i];
     for(j=0;j<=n-1;j++)
     if(j!=i) a[i]*=(xx-x[j])/(x[i]-x[j]);
     yy+=a[i];
   }
 free(a);
 return yy;
}
main()
{ int i,n;
 float x[20],y[20],xx,yy;
 printf("Input n:");
 scanf("%d",&n);
 if(n>=20) {printf("Error!The value of n must in (0,20)."); getch();return 1;}
 if(n<=0) {printf("Error! The value of n must in (0,20)."); getch(); return 1;}
 for(i=0;i<=n-1;i++)
 { printf("x[%d]:",i);
    scanf("%f",&x[i]);
 }
 printf("\n");
 for(i=0;i<=n-1;i++)
 { printf("y[%d]:",i);scanf("%f",&y[i]);}
 printf("\n");
 printf("Input xx:");
 scanf("%f",&xx);
 yy=lagrange(x,y,xx,n);
 printf("x=%f,y=%f\n",xx,yy);
 getch();
}

#include <stdio.h>
#include <conio.h>
#include <alloc.h>
void difference(float *x,float *y,int n)
{ float *f;
 int k,i;
 f=(float *)malloc(n*sizeof(float));
 for(k=1;k<=n;k++)
 { f[0]=y[k];
    for(i=0;i<k;i++)
      f[i+1]=(f[i]-y[i])/(x[k]-x[i]);
    y[k]=f[k];
 }
 return;
}
main()
{ int i,n;
 float x[20],y[20],xx,yy;
 printf("Input n:");
 scanf("%d",&n);
 if(n>=20) {printf("Error! The value of n must in (0,20)."); getch(); return 1;}
 if(n<=0) {printf("Error! The value of n must in (0,20).");getch(); return 1;}
 for(i=0;i<=n-1;i++)
 { printf("x[%d]:",i);
    scanf("%f",&x[i]);
 }
   printf("\n");
 for(i=0;i<=n-1;i++)
 { printf("y[%d]:",i);scanf("%f",&y[i]);}
 printf("\n");
 difference(x,(float *)y,n);
 printf("Input xx:");
 scanf("%f",&xx);
 yy=y[20];
 for(i=n-1;i>=0;i--) yy=yy*(xx-x[i])+y[i];
 printf("NewtonInter(%f)=%f",xx,yy);
 getch();
}

#include<stdio.h>
#include <math.h>
#define N 20
int main()
{ int n,i,j,k;
 int mi,tmp,mx;
 float a[N][N],b[N],x[N];
 printf("\nInput n:");
 scanf("%d",&n);
 if(n>N)
 { printf("The input n should in(0,N)!\n");
    getch();
    return 1;
 }
 if(n<=0)
 { printf("The input n should in(0,N)!\n");
    getch();
    return 1;
 }
 printf("Now 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("Now input b(i),i,j=0...%d:\n",n-1);
 for(i=0;i<n;i++)
 scanf("%f",&b[i]);
 for(i=0;i<n-2;i++)
 { for(j=i+1,mi=i,mx=fabs(a[i][j]);j<n-1;j++)
    if(fabs(a[j][i])>mx)
    { mi=j;
      mx=fabs(a[j][i]);
    }
    if(i<mi)
    { tmp=b[i];b[i]=b[mi];b[mi]=tmp;
      for(j=i;j<n;j++)
      { tmp=a[i][j];
        a[i][j]=a[mi][j];
        a[mi][j]=tmp;
      }
    }
    for(j=i+1;j<n;j++)
    { tmp=-a[j][i]/a[i][i];
      b[j]+=b[i]*tmp;
      for(k=i;k<n;k++)
      a[j][k]+=a[i][k]*tmp;
    }
 }
 x[n-1]=b[n-1]/a[n-1][n-1];
 for(i=n-2;i>=0;i--)
 { x[i]=b[i];
    for(j=i+1;j<n;j++)
    x[i]-=a[i][j]*x[j];
    x[i]/=a[i][i];
 }
 for(i=0;i<n;i++)
 printf("Answer:\n x[%d]=%f\n",i,x[i]);
 getch();
 return 0;
}
 
 
#include<math.h>
#include<stdio.h>
#define NUMBER 20
#define Esc   0x1b
#define Enter 0x0d
 
float A[NUMBER][NUMBER+1] ,ark;
int flag,n;
exchange(int r,int k);
float max(int k);
message();
 
main()
{
   float x[NUMBER];     
   int r,k,i,j;
   char celect;
   clrscr();
  
   printf("\n\nUse Gauss.");
   printf("\n\n1.Jie please press Enter.");
   printf("\n\n2.Exit press Esc.");
   celect=getch();
   if(celect==Esc)
     exit(0);
   printf("\n\n input n=");
   scanf("%d",&n);
     printf(" \n\nInput matrix A and B:");
   for(i=1;i<=n;i++)
   {
    printf("\n\nInput a%d1--a%d%d and b%d:",i,i,n,i);
       
    for(j=1;j<=n+1;j++)        scanf("%f",&A[i][j]);
   }
   for(k=1;k<=n-1;k++)                      
   {
   ark=max(k);
    if(ark==0)                  
    {
      printf("\n\nIt's wrong!");message();
    }
    else if(flag!=k)
     exchange(flag,k);
     for(i=k+1;i<=n;i++)
     for(j=k+1;j<=n+1;j++)
     A[i][j]=A[i][j]-A[k][j]*A[i][k]/A[k][k];
   }
   x[n]=A[n][n+1]/A[n][n];
   for( k=n-1;k>=1;k--)
   {
     float me=0;
     for(j=k+1;j<=n;j++)
     {
       me=me+A[k][j]*x[j];
     }
       x[k]=(A[k][n+1]-me)/A[k][k];
   }
   for(i=1;i<=n;i++)
   {
     printf(" \n\nx%d=%f",i,x[i]);
   }
   message();
}
 
exchange(int r,int k)      
{
 int i;
 for(i=1;i<=n+1;i++)
    A[0][i]=A[r][i];
 for(i=1;i<=n+1;i++)
    A[r][i]=A[k][i];
 for(i=1;i<=n+1;i++)
    A[k][i]=A[0][i];
}
 
float max(int k)         
{
 int i;
 float temp=0;
 for(i=k;i<=n;i++)
    if(fabs(A[i][k])>temp)
    {
      temp=fabs(A[i][k]);
      flag=i;
    }
 return temp;
}
 
message()                                    
{
 printf("\n\n Go on Enter ,Exit press Esc!");
 switch(getch())
 {
   case Enter: main();
   case Esc: exit(0);
   default:{printf("\n\nInput error!");message();}
 }
}