newton_cz.cpp

这是计算方法上的所有算法

#include<stdio.h>
#include<iostream.h>
#include<conio.h>
#define N 4
//static 
int checkvaild(double x[],int n)
{
	int i,j;
	for(i=0;i<n+1;i++) 
	{
		for(j=i+1;j<n+1;j++)
			if(x[i]==x[j])
				return -1;
	}
	return 1;
}

void chashang(double x[],double y[],double f[][N+1])
{//求差商 
	//double f[][N+1];
	int i,j,t=0;
	//f1[0][0]=y[0];
	for(i=0;i<N+1;i++)
	{
		f[i][0]=y[i];
	}
	for(j=1;j<N+1;j++)
	{
		for(i=0;i<N-j+1;i++)		
			f[i][j]=(f[i+1][j-1]-f[i][j-1])/(x[t+i+1]-x[i]);
		t++;
	}
}

double compvalue(double t[][N+1],double x[],double varx)
{
	int i,j,r=0;
	double sum=t[0][0],m[N+1]={sum,1,1,1,1};
	printf("i\txi\t    F(xi)\t   1阶\t    2阶\t\t3阶\t    4阶\n");
	printf("--------------------------------------------------------------------------------");
	for(i=0;i<N+1;i++)
	{
		r=i;
		printf("x%d\t%f    ",i,x[i]);
		for(j=0;j<=i;j++)
		{
			printf("%f    ",t[r][j]);
			r--;
		}
		printf("\n");
	}

    printf("--------------------------------------------------------------------------------");/**/
	printf("N(x) =\n");
	printf("      %f\n",t[0][0]);
	for(i=1;i<N+1;i++)
	{
		for(j=0;j<i;j++)
		m[i]=m[i]*(varx-x[j]);
		m[i]=t[0][i]*m[i];		
		sum=sum+m[i];
	}

	for(i=1;i<N+1;i++)	
	{	printf("     +%f*",t[0][i]);
		for(j=0;j<i;j++)
		printf("(x-%f)",x[j]);
		printf("\n");
	}
	return sum;
}


void main()
{
	double varx,f[N+1][N+1];
	double x[N+1]={0.4,0.55,0.8,0.9,1};
	double y[N+1]={0.41075,0.57815,0.88811,1.02652,1.17520};
	checkvaild(x,N);
	chashang(x,y,f);
	varx=0.5;
	//compvalue(f,x,varx);
	if(checkvaild(x,N)==1)
	{
		chashang(x,y,f);
		printf("\n\n牛顿插值结果:  P(%f)=%f\n",varx,compvalue(f,x,varx));
	}
	else
		printf("输入的插值节点的x值必须互异!");
	getch();
}