jacobi.cpp

计算方法雅可比公式

#include<iostream.h>
#include<math.h>
#define MAX_N 20          
#define MAXREPT 100       
#define epsilon 0.00001   
void main()
{
	short i,j,k,n;
	double a[MAX_N][MAX_N],c[MAX_N],x[MAX_N][MAX_N];
	double temp=1,temp1,temp2;
	cout<<"Input n value(dim of Ax=c):";
	cin>>n;
	cout<<"Now input the matrix a(i,j),i,j=1,...,"<<n<<":";
	for(i=1;i<=n;i++)
	{
		for(j=1;j<=n;j++)
		{
			cin>>a[i][j];
		}
	}
	cout<<"Now input the matrix c(i),i=1,...,"<<n<<":";
	for(i=1;i<=n;i++)
	{
		cin>>c[i];
	}
	cout<<"Now input the begin matrix x[i][0],i=1,...,"<<n<<":";
	for(i=1;i<=n;i++)
	{
		cin>>x[i][0];
	}
	for(k=0;k<=MAXREPT&&temp>=epsilon;k++)
	{
		for(i=1;i<=n;i++)
		{
			temp1=temp2=0;
			for(j=1;j<=i-1;j++)
			{
				temp1=temp1+a[i][j]*x[j][k+1];
			}
			for(j=i+1;j<=n;j++)
			{
				temp2=temp2+a[i][j]*x[j][k];
			}
			x[i][k+1]=(c[i]-temp1-temp2)/a[i][i];
		}
		for(i=1;i<n;i++)
		{
			if((x[i][k+1]-x[i][k])>(x[i+1][k+1]-x[i+1][k])||(x[i][k+1]-x[i][k])<(x[i+1][k]-x[i+1][k+1]))
			{
				if((x[i][k+1]-x[i][k])>=0)
					temp=x[i][k+1]-x[i][k];
				else
					temp=x[i][k]-x[i][k+1];
			}
			else
			{
				if((x[i+1][k+1]-x[i+1][k])>=0)
					temp=x[i+1][k+1]-x[i+1][k];
				else
					temp=x[i+1][k]-x[i+1][k+1];
			}
		}
	}
	cout<<"k="<<k<<endl;
	cout<<"Solve...x_i="<<endl;
	for(i=1;i<=n;i++)
	{
		cout<<x[i][k]<<endl;
	}
}