实验1拉格朗日插值与牛顿插值

西华数学与计算机学院上机实践报告课程名称：数值计算方法B 年级：2009级 上机实践成绩：指导教师：严常龙 姓名：李艳萍上机实践名称：拉格朗日插值和牛顿插值法 学号：332009090101132上机实践日期：2011.11.30上机实践编号：1 上机实践时间：一、目的1．通过本实验加深对拉格朗日插值和牛顿插值法构造过程的理解；2．能对上述两种插值法提出正确的算法描述编程实现。二、内容与设计思想自选插值问题，编制一个程序，分别用拉格朗日插值法和牛顿插值法求解某点的函数近似值。已知的数据表如下，求扫0・63处的函数值z=f(t)。ixiyiixiyi10.100.90483760.570.56552520.150.86070870.700.49658530.250.77880180.850.42741540.400.67032090.930.39455450.500.606531101.000.367879三、使用环境操作系统：软件环境：四、核心代码及调试过程拉格朗日插值算法#include<stdio.h>#include<conio.h>#include<malloc.h>floatlagrange(float*x,float*y,floatxx,intn) /*拉格朗日插值算法*/{inti,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);returnyy;}main(){inti,n;floatx[20],y[20],xx,yy;printf("Inputn:");scanf("%d",&n);if(n>=20){printf("Error!Thevalueofnmustin(0,20).");getch();return1;}if(n<=0){printf("Error!Thevalueofnmustin(0,20).");getch();return1;}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("Inputxx:");scanf("%f",&xx);yy=lagrange(x,y,xx,n);printf("x=%f,y=%f\n",xx,yy);getch();}牛顿插值#include<stdio.h>#include<conio.h>#include<malloc.h>voiddifference(float*x,float*y,intn){float*f;intk,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(){inti,n;floatx[20],y[20],xx,yy;printf("Inputn:");scanf("%d",&n);if(n>=20){printf("Error!Thevalueofnmustin(0,20).");getch();return1;}if(n<=0){printf("Error!Thevalueofnmustin(0,20).");getch();return1;}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("Inputxx:");scanf("%f",&xx);yy=y[20];for(i=n-1;i>=0;