#include<stdio.h>
#include<stdlib.h>
#include<conio.h>
#include<time.h>
#include<math.h>
#define DIM 6
#define MI 1000
#define EPSILON 1.0e-10
int gseidel(double A[DIM][DIM],double b[DIM],double x[DIM])
{
static int first=0;
int i,j,k;
static double x1[DIM],norm;
norm=0.0;
if(first==0)
{
for(i=0;i<DIM;i++){
x[i]=rand();
norm=norm+x[i]*x[i];}
norm=sqrt(norm);
for(i=0;i<DIM;i++)x[i]=x[i]/norm;
first=1;
}
for(k=0;k<MI;k++)
{
for(i=0;i<DIM;i++)
{
x1[i]=b[i];
for(j=0;j<i;j++)x1[i]=x1[i]-A[i][j]*x1[j];
for(j=i+1;j<DIM;j++) x1[i]=x1[i]-A[i][j]*x[j];
x1[i]=x1[i]/A[i][i];}
norm=0.0;
for(i=0;i<DIM;i++)norm=norm+(x1[i]-x[i])*(x1[i]-x[i]);
norm=sqrt(norm);
for(i=0;i<DIM;i++)x[i]=x1[i];
if(norm<EPSILON) goto endd;
}
endd:return (k);
}
void main()
{
int i,itime,iter;
char ifdoyn;
static double A[DIM][DIM]= {{1,-0.25,-0.5,0,0,0},
{ -0.25,1,0,-0.5,0,0},
{ -0.25,0,1,-0.25,-0.25,0},
{ 0,-0.25,-0.25,1,0,-0.25},
{0,0,-1,0,2.05,-0.5},
{0,0,0,-1,-0.5,2.05},
{0,0,-1/2.05,0,1,-0.5/2.05},
{0,0,0,1/2.05,-0.5/0.25,1}};
static double x[DIM],b[DIM]={25.00,125.00,25.00,125.00,52.50,252.50,52.50/2.05,252.50/2.05};
itime=0;
printf("高斯-塞德尔迭代法\n");
again:iter=gseidel(A,b,x);
itime=itime+iter;
if(iter<MI) itime=itime+1;
printf("迭代次数%3d次\n",itime);
for(i=0;i<DIM;i++)printf("%15.10f",x[i]);
if(iter<MI)printf("成功\n");
else
{
printf("是否继续迭代?y/n");
ifdoyn==getchar();
if(ifdoyn=='y'||ifdoyn=='Y')goto again;
}}