gaussseidel迭代法解方程组.txt

数值方法课程中的程序

#include<iostream.h>
#include<math.h>
int K;
void GaussSeidel(double A[6][6],double x[2][6],double b[6],int n)
{  int i,j,k,r;
   double t,s,h;
   
   for(k=1;;k++)
   {  for(i=0;i<n;i++)
      {  s=0.0;  
         for(j=0;j<=i-1;j++)
         {  if(k%2==0) 
            s=s+A[i][j]*x[1][j];
            else s=s+A[i][j]*x[0][j];
         }
         
         t=0.0;
         for(j=i+1;j<=n-1;j++)
         {  if(k%2==0)
            t=t+A[i][j]*x[0][j];
            else t=t+A[i][j]*x[1][j];
         }
         
         if(k%2==0)
         {  x[1][i]=(b[i]-s-t)/A[i][i];}
         else x[0][i]=(b[i]-s-t)/A[i][i];
      }
      
      h=0.0;
      for(r=0;r<n;r++)
      {  h=h+(x[1][r]-x[0][r])*(x[1][r]-x[0][r]);}
      if(sqrt(h)<=(1e-5))
      break;
   }
   
   cout<<k<<endl;
   K=k;

}

void main()
{  int i,j,n=6;
   double b[6]={0,5,0,6,-2,6};
   double A[6][6]={{4,-1,0,-1,0,0},{-1,4,-1,0,-1,0},{0,-1,4,0,0,-1},{-1,0,0,4,-1,0},{0,-1,0,-1,4,-1},{0,0,-1,0,-1,4}};
   double x[2][6]={{0,0,0,0,0,0},{1,1,1,1,1,1}};
   
   GaussSeidel(A,x,b,n);
   for(i=0;i<n;i++)
   {  if(K%2==0)
      cout<<x[1][i]<<endl;
      else cout<<x[0][i]<<endl;
   }
}