main.cpp

研究生期间上《数值计算方法》课的作业

#include <iostream>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define MaxD 21

using namespace std;

int N;
float X[MaxD];
float Y[MaxD];

float F(float x)
{
    return 1/(1+25*pow(x,2));
}

float Lagrange(float x)
{
    float retVal = 0;
    float t = 0;
    int k=0,j=0;
    
    for(k=0; k<=N; k++)
    {
        t = 1.0;
        for(j=0; j<=N; j++)
        {
            if(j!=k)
            {
                t = t*(x-X[j])/(X[k]-X[j]);
            }
        }
        retVal = retVal + t*Y[k];
    }
    return retVal;
}

int main(int argc, char *argv[])
{
    int i=0;
    float length = 0;
    float tempX = 0;
    float tempY = 0;
    
    printf("请输入等分数（不大于20）：");
    scanf("%d",&N);
    
    length = 2.0/N;
    printf("计算节点处的函数值... ...\n");
    for(i=0; i<=N; i++)
    {
        X[i] = length*i - 1;
        Y[i] = F(X[i]);
        printf("X[%d]=%5f     ",i,X[i]);
        printf("Y[%d]=%5f\n",i,Y[i]);
    }
    system("PAUSE");
    
    for(i=0; i<10; i++)
    {        
        tempX = (rand()%10)/9.5;
        tempY = Lagrange(tempX);
        printf("X =  %5f   Y = %5f\n",tempX,tempY);
        tempY = Lagrange((-1)*tempX);
        printf("X = %5f   Y = %5f\n",(-1)*tempX,tempY);
    }	
    system("PAUSE");
    return 0;
}