[数值算法]Lagrange插值法

        Lagrange插值法并不是十分实用的插值法,通常是在分段插值中使用,当插值结点过多时,会出现数据不稳定的龙格现象.

 

#include "Lagrange.h"

#include "myAssert.h"

#include <stdlib.h>

#include <stdio.h>

Type lagrangeInsert(Type *xArr,Type *yArr,Type x,int n)

{

       Type tmpSum=Type_Zero,sum=Type_Zero;

       int i=0,j=0;

       asserts(xArr!=NULL,"xArr passed in is null/n");

       asserts(yArr!=NULL,"yArr passed in is null/n");

       for (i=0;i<n;i++)

       {

              tmpSum=yArr[i];

              for(j=0;j<n;j++)

                     if(j!=i)tmpSum*=(x-xArr[j])/(xArr[i]-xArr[j]);

              sum+=tmpSum;

       }

       return sum;

}

 

/*test*/

#include "Lagrange.h"

#include "stdio.h"

#include "string.h"

void main()

{

       double x1[]={0.4,0.5,0.6,0.7};

       double y1[]={-0.916291,-0.693147,-0.510826,-0.356675};

       double ans;

       clrscr();

       ans=lagrangeInsert(x1,y1,0.54,4);//4表示所插值出的是四次多项式.

       printf("The answer of lagrangeInsert is:%f/n",ans);

}