jacobi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 Jacobi(double A[6][6],double x[2][6],double b[6],int n)
{  int i,j,k,r;
   double s,t;

   for(k=1;;k++)
   {  for(i=0;i<n;i++)
      {  s=0.0;
         for(j=0;j<n;j++)
         {  if(j!=i)
            {  if(k%2==0)
               s=s+A[i][j]*x[1][j];
               else s=s+A[i][j]*x[0][j];
            }
         }
      
         if(k%2==0)
         {  x[0][i]=(b[i]-s)/A[i][i];}
         else x[1][i]=(b[i]-s)/A[i][i];
      }
        
      t=0.0;
      for(r=0;r<n;r++)
      {  t=t+(x[1][r]-x[0][r])*(x[1][r]-x[0][r]);}
      if(sqrt(t)<=(1e-5))
      break;
   }
   
   K=k;
   cout<<k<<endl;
}

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]={{1,1,1,1,1,1},{0,0,0,0,0,0}};
   
   Jacobi(A,x,b,n);
   for(i=0;i<n;i++)
   {  if(K%2==0)
      cout<<x[0][i]<<endl;
      else cout<<x[1][i]<<endl;
   }
}