seidel迭代法.cpp

计算方法程序,包括高斯列主元法,复化simpson,标准四阶龙格库塔,Seidel迭代,Romberg算法

#include<iostream.h>
#include<math.h>

double d(double *x,double *x0,int n)         //求范数
{
	double m=0;
	for(int i=0;i<n;i++)
		if(m<fabs(x[i]-x0[i]))m=fabs(x[i]-x0[i]);
	return m;
}

void main()
{
	cout<<"-----------------------Seidel迭代-------------------------"<<endl;
a1:	int n,N,i,j,k;
	double e,*x,*x0,*b,*a;
	cout<<"输入未知数个数n:"<<endl;
	cin>>n;
	cout<<"输入误差限e:"<<endl;
	cin>>e;
	cout<<"输入最大允许迭代次数N:"<<endl;
	cin>>N;
	x=new double[n];
    x0=new double[n];
	a=new double[n*n];
	b=new double[n];
	cout<<"输入系数矩阵:\n";
	for(i=0;i<n*n;i++)
	{
		cout<<"a["<<i<<"]=";
		cin>>a[i];
	}
	cout<<"输入常数项矩阵:\n";
	for(i=0;i<n;i++)
	{
		cout<<"b["<<i<<"]=";
		cin>>b[i];
	}
	cout<<"输入初始未知数的值:\n";
	for(i=0;i<n;i++)
	{
		cout<<"x0["<<i<<"]=";
		cin>>x0[i];
		x[i]=x0[i];
	}
	for(k=0;;k++)
	{                       //迭代
		for(i=0;i<n;i++)
		{
            x[i]=b[i];
			for(j=0;j<n;j++)
			{
				if(j!=i)x[i]-=a[i*n+j]*x[j];
			}
			x[i]/=a[i*n+i];
		}
		if(d(x,x0,n)<e)break;       //判断      
		if(k>=N)       //报错
		{         
			cout<<"超过最大迭代次数,迭代失败!"<<endl;
			break;
		}
		else{cout<<"第"<<k<<"次迭代成功!"<<endl;}
		for(i=0;i<n;i++)x0[i]=x[i];           //准备
	}
	if(k<N)
	{
		cout<<"方程组的解为:"<<endl;
		for(i=0;i<n;i++)cout<<"x["<<i+1<<"]="<<x[i]<<endl;
	}
	delete[]x;
	delete[]x0;
	delete[]a;
	delete[]b;
	char out='y';
	cout<<"继续?y/n"<<endl;
	cin>>out;
	if(out!='n') goto a1;
}