gaosi.cpp

计算方法《高斯定理》

#include<iostream.h>
#define	MAX_N	20
void main()
{
	int i,j,k,n,m;
    float a[MAX_N][MAX_N],b[MAX_N],x[MAX_N],L[MAX_N][MAX_N],temp;
	cout<<"Input n value(dim of Ax=b):";
	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 b(i),i =1,…,"<<n<<":";
	for(i=1;i<=n;i++)
	{
		cin>>b[i];
	}
	for(k=1;k<=n-1;k++)
	{
		for(i=k;i<=n-1;i++)
		{
			if(a[i][k]>=a[i+1][k])
			{
				m=i;
			}
			else
			{
				m=i+1;
			}
		}
		for(j=k;j<=n;j++)
			{
				temp=a[k][j];
				a[k][j]=a[m][j];
				a[m][j]=temp;
			}
		temp=b[k];
		b[k]=b[m];
		b[m]=temp;
		for(i=k+1;i<=n;i++)
		{
			L[i][k]=a[i][k]/a[k][k];
			for(j=k+1;j<=n;j++)
			{
				a[i][j]=a[i][j]-L[i][k]*a[k][j];
			}
			b[i]=b[i]-L[i][k]*b[k];
		}
	}
	x[n]=b[n]/a[n][n];
	for(i=n-1;i>=1;i--)
	{
		x[i]=b[i];
		for(j=i+1;j<=n;j++)
		{
			x[i]=x[i]-a[i][j]*x[j];
		}
		x[i]=x[i]/a[i][i];
	}
	cout<<"Solve...x_i="<<endl;
	for(i=1;i<=n;i++)
	{
		cout<<x[i]<<endl;
	}
}