sor.cpp

SOR算法的基本思想以及详细的代码实现和运行情况。

#include<iostream.h>
#include<stdio.h>
#include<math.h>
double max(double *x,double *x1,int n)
{
	double m=fabs(x[0]-x1[0]);
	for(int i=1;i<n;i++)
		if(fabs(x[i]-x1[i])>m)
			m=fabs(x[i]-x1[i]);
	return m;
}
void diedai(double **A,double *x,double *b,int n,double w)
{
	for(int i=0;i<n;i++)
	{
		double s=0.0;
		for(int j=0;j<n;j++)
		s+=A[i][j]*x[j];
		x[i]=x[i]+w*(b[i]-s)/A[i][i];
	}
}
main()
{
	int i,j;
	double w;
	int N;
	int n;
	cout<<"请输入矩阵阶数：";
	cin>>n;
	double **A;
	A=new double*[n];
	for(i=0;i<n;i++)
		A[i]=new double[n];
	double *x=new double[n];
	double *x1=new double[n];
	double *b=new double[n];
	for(i=0;i<n;i++)
		x[i]=0;
	cout<<"请输入A、b以及松弛因子w：";
	for(i=0;i<n;i++)
		for(j=0;j<n;j++)
		{
			cout<<"A["<<i<<"]["<<j<<"]=";
			cin>>A[i][j];
		}
	for(i=0;i<n;i++)
	{
		cout<<"b["<<i<<"]=";
		cin>>b[i];
	}
	cout<<"w=";
	cin>>w;
	//for(i=0;max(x,x1,n)<=1e-5;i++)
	i=0;
	do{
		for(j=0;j<n;j++)
			x1[j]=x[j];
		diedai(A,x,b,n,w);
		
		i++;
	}while(max(x,x1,n)>=0.00001);
	cout<<"经过"<<i<<"次迭代后结果为："<<endl;
	for(i=0;i<n;i++)
		cout<<"x["<<i+1<<"]="<<x[i]<<" ";
	cout<<endl;
	for(i=0;i<n;i++)
		delete[] A[i];
	delete[] x;
	delete[] x1;
	delete[] b;
	return 0;
}