Gauss-Seidel Iterative Method

/*      The following C program implements Gauss-Seidel iterative method for

         finding the solution of a set of linear simultaneous equations. The number of

        equations and the coefficient matrix are read as input. The results are printed

        properly.        */

#include<stdio.h>

#include<math.h>

#include<conio.h>

#define maximum 10

#define minvalue 0.0005

void main()

{

 float augmentedmatrix[maximum][maximum] ;  /* 2D array declared to store augmented co-efficient matrix */

 float result, maxdiff, diff, pivotalrow, pivotalelement, t ;

 float solutions[maximum] ;    /* 1D array declared to store solutions of the simultaneous equations */

 int i, j, k, noofequations; 
  /* declaring counter variables for loops */

 clrscr();

printf("\n   GAUSS-SEIDEL ITERATIVE METHOD\n\n");

 printf("\n Enter the number of total equations to be provided as input : \n");

 scanf("%d",&noofequations);

 /* storing augmented co-efficient matrix as a matrix of dimension

    (noofequations)x(noofequations+1) in 2D array */

 printf("\n Enter the augmented co-efficient matrix : \n");

 for(i=0; i<noofequations; i++)

  for(j=0; j<=noofequations; j++)

            scanf("%f",&augmentedmatrix[i][j]) ;

 /* pivoting the matrix */

 for(i=0; i<noofequations-1; i++)

 {

  pivotalelement=fabs(augmentedmatrix[i][i]);

  pivotalrow=i;

  for(j=pivotalrow+1; j<noofequations; j++)

            if(pivotalelement<fabs(augmentedmatrix[j][i]))

            {

              pivotalelement = fabs(augmentedmatrix[j][i]);

              pivotalrow=j;

            }

  for(j=0;j<=noofequations; j++)

  {

            t=augmentedmatrix[i][j];

            augmentedmatrix[i][j]=augmentedmatrix[pivotalrow][j];

            augmentedmatrix[pivotalrow][j]=t;

  }

 }

/* using Gauss-Seidel iterative method */

 maxdiff=minvalue ;

 k=0;

 while(maxdiff>=minvalue)

 {

  ++k;

  maxdiff = 0;

  /* rowwise scanning, substituting estimates of (nofequations-i) unknowns

      to get X_i in the i^th row */

  for(i=0; i<noofequations; i++)

  {

   result=augmentedmatrix[i][noofequations] ;

  /* columnwise scanning, to get the solution of i^th unknown in ith row */

   for(j=0; j<noofequations; j++)

     if(i!=j)

            result-=augmentedmatrix[i][j]*solutions[j];

  

   result/=augmentedmatrix[i][i] ;

   diff=solutions[i]-result;

            if(fabs(diff)>maxdiff)

                        maxdiff = fabs(diff) ;

   solutions[i]=result;

  }                               /* end of outer for loop */

  printf("\n\n %d", k) ;          /* gives the no. of iterations performed */

  for(j=0; j<noofequations; j++)

            printf(" %f",solutions[j]) ;   /* current estimated solutions will be printed */

  printf(" %f",maxdiff);

 }                              /* end of outermost while loop */

 printf("\n\n\n");

 /* printing solutions */

 for(i=0; i<noofequations; i++)

  printf("  X%d  =  %.3f \n", i, solutions[i]) ;

 end: getch() ;

 }

SAMPLE OUTPUT:

Solving the following set of linear simultaneous equations by Gauss-Seidel iteration:

  3x₀ + 2x₁ + 6x₂ = 17

15x₀ + 6x₁ + 7x₂ = 24

2x₀ - 4x₁ - 2x₂ = 4