Gauss Elimination Method

Algorithm:Gauss Elimination Method

GaussElimination(a,n)
{
Here a denotes the coefficient matrix and n is the size of the matrix.
for(k=0 to k<n)
{
for(r=k+1 to r<=n-1)
{
m=a[r][k]/a[k][k]
for(c=0 to c<=n-1)
{
a[r][c]=a[r][c]-m*a[k][c]
}
}
}
x[n-1]=a[n-1][n]/a[n-1][n-1]		// Here x is the constant matrix									
for(i=n-2 to igt;=0)
{
sum=0
for(j=i+1 to j<=n-1)
{
sum=sum+a[i][j]*x[j]
}
x[i]=(a[i][n]-sum)/a[i][i]
}
for(i=0 to i<n)
print(x[i])					// Prints the roots
}



C Program For Gauss Elimination Method

Source Code:

#include<stdio.h>
#include<conio.h>
#include<alloc.h>


void show(float **A,int n1)
{
   int i,j;
   for(i=1;i<=n1;i++)
   {
      for(j=1;j<=n1+1;j++)
      {
  printf("\t%g",A[i][j]);
      }
      printf("\n");
   }
}


void gauss_eli(float **A,int n)
{
   int k,i,j,row,col,n1;
   float m,sum,X[30];
   n1=n;
   for(k=1;k<=n-1;k++)
   {
      for(row=k+1;row<=n;row++)
      {
  m=(A[row][k])/(A[k][k]);
  for(col=1;col<=n+1;col++)
  {
     A[row][col]=A[row][col]-m*A[k][col];
  }
      }
      printf("\nStep %d:",k);
      show(A,n1);
      printf("--------------------------------------");
   }
   X[n]=(A[n][n+1])/(A[n][n]);
   printf("\nLast step:\n");
   show(A,n1);
   for(i=n-1;i>=1;i--)
   {
      sum=0;
      for(j=i+1;j<=n;j++)
      {
 sum=sum+A[i][j]*X[j];
      }
      X[i]=(A[i][n+1]-sum)/(A[i][i]);
   }
   for(i=1;i<=n;i++)
   {
      printf("\nX%d=%g",i,X[i]);
   }
}

void main()
{
   int n,r,c,j,i;
   float **A;
   clrscr();
   printf("\nEnter number of variables:");
   scanf("%d",&n);
   r=n+1;
   c=n+2;
   A=(float **)malloc(sizeof(float *)*r);
   for(i=1;i<=r;i++)
   {
      A[i]=(float *)malloc(sizeof(float)*c);
   }
   for(i=1;i<=n;i++)
   {
      for(j=1;j<=n+1;j++)
      {
   printf("\nEnter term %d of equation %d:",j,i);
   scanf("%f",&A[i][j]);
      }
   }
   gauss_eli(A,n);
   getch();
}



 Output :

Enter number of variables:3

Enter term 1 of equation 1:2

Enter term 2 of equation 1:-3

Enter term 3 of equation 1:4

Enter term 4 of equation 1:8

Enter term 1 of equation 2:1

Enter term 2 of equation 2:1

Enter term 3 of equation 2:4

Enter term 4 of equation 2:15

Enter term 1 of equation 3:3

Enter term 2 of equation 3:4

Enter term 3 of equation 3:-1

Enter term 4 of equation 3:8

Step 1:
        2       -3      4       8
        0       2.5     2       11
        0       8.5     -7      -4
--------------------------------------
Step 2:
        2       -3      4       8
        0       2.5     2       11
        0    -2.38419 -13.8   -41.4
--------------------------------------
Last step:

        2       -3      4       8
        0       2.5     2       11
        0   -2.38419   -13.8   -41.4

X1=1
X2=2
X3=3