多项式拟合.cpp

计算方法程序:多项式拟合

#include <conio.h>
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <Malloc.h>
#include <iostream.h>
double f(double x)
{
 return exp(x)+10*x-2;
}
double f(double x,double y)
{
   return y-2.0*x/y;
}
void main()
{
	cout<<"******多项式拟合******"<<endl;
	int n,N,i,j,k,d;
	double **a,*b,*S1,*S2,*x,*y,temp,max=0,S=0;
	cout<<"请输入数据个数：";
	cin>>n;
	x=(double *)malloc(n*sizeof(double));
	y=(double *)malloc(n*sizeof(double));
	cout<<"请输入数据："<<endl;
	for(i=0;i<n;i++)
	{
		cout<<"x"<<i+1<<"=";
		cin>>x[i];
		cout<<"y"<<i+1<<"=";
		cin>>y[i];
	}
	cout<<"请输入多项式次数："<<endl;
	cin>>N;
	if(n<N) {cout<<"次数不正确!不足以达到此次数!"<<endl;exit(0);}
	S1=(double *)malloc((2*N+1)*sizeof(double));
	S2=(double *)malloc((N+1)*sizeof(double));
	a=(double **)malloc((N+1)*sizeof(double *));
	for(i=0;i<=N;i++)
		*(a+i)=(double *)malloc((N+1)*sizeof(double));
	b=(double *)malloc((N+1)*sizeof(double));
	for(i=0;i<=2*N;i++)
	{
	   S1[i]=0;
	   if(i<=N) S2[i]=0;
	}
	for(i=0;i<=2*N;i++)
	{
		for(j=0;j<n;j++)
		{
			S1[i]=S1[i]+pow(x[j],i);
			if(i<=N) S2[i]=S2[i]+pow(x[j],i)*y[j];
		}
	}
	for(i=0;i<=N;i++)
	{
		for(j=0;j<=N;j++)
			a[i][j]=S1[i+j];
		b[i]=S2[i];
	}
    	for(k=0;k<=N;k++)
	{
        if(fabs(a[k][k])<0.000001)
		{
			for(i=k+1;i<=N;i++)
                if(fabs(a[i][k])>max) {max=a[i][k];d=i;}
			for(j=k;j<=N;j++)
			{temp=a[k][j];a[k][j]=a[d][j];a[d][j]=temp;}
			max=0;
		}
		for(j=k+1;j<=N;j++)
			a[k][j]=1.0*a[k][j]/a[k][k];
		b[k]=1.0*b[k]/a[k][k];
		for(i=k+1;i<=N;i++)
		{
			for(j=k+1;j<=N;j++)
				a[i][j]=a[i][j]-a[i][k]*a[k][j];
		    b[i]=b[i]-a[i][k]*b[k];
		}
	}
	for(i=N-1;i>=0;i--)
	{
		for(j=i+1;j<=N;j++)
            S+=a[i][j]*b[j];
		b[i]=b[i]-S;
		S=0;
	}
	cout<<"多项式各项为："<<endl;
	for(i=0;i<=N;i++)
		cout<<"a"<<i<<"="<<b[i]<<"  ";
	cout<<endl;
	free(b);
	for(i=0;i<=N;i++)
		free(*(a+i));
	free(x);
	free(y);
	free(S1);
	free(S2);
}