[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);

}