My code in c for gauss jacobi isn't working? why is it so?

Question

#include<stdio.h>

#include<stdlib.h>

#include<math.h>

int main()

{

int a[5][5],b[5],n,i,j,flag=1,key=0;

char c;

float e,sum,xo[10],x1[10],s;

setbuf(stdout,NULL);

printf("This program illustrates Gauss Jacobi Method in C :\n");

printf("Enter the dimension of the coefficient matrix A:");

scanf("%d",&n);

printf("Enter the %d elements of the coefficient matrix A:",n*n);

for(i=0;i<n;i++)

for(j=0;j<n;j++)

scanf("%d",&a[i][j]);

printf("Enter the elements of the constant matrix B:");

for(i=0;i<n;i++)

scanf("%d",&b[i]);

printf("The given system of linear equations is\n");

for(i=0;i<n;i++)

{

for(j=0;j<n;j++)

{

if((j==0 || j==1 ) && (a[i][j+1]>0))

c='+';

else if(j==2)

c='=';

printf("%dx%d\t%c",a[i][j],j+1,c);

}

printf("%d",b[i]);

printf("\n");

}

    for(i=0;i<n;i++)

    {

        for(j=0;j<n;j++)

        {

            if(i!=j)

               s=s+a[i][j];

        }

        if(fabs(a[i][i])<fabs(s))

        {

            flag=0;

            break;

        }

    }

if(flag==0)

{

printf("Error!The given system of linear equations is not diagonally dominant.");

exit(0);

}

else

{   

    printf("The given system of linear equations is diagonally dominant.a\n");

printf("Enter the initial approximate solution to the given system:");

for(i=0;i<n;i++)

{

scanf("%f\t",&xo[i]);

}

for(i=0;i<n;i++)

{

printf("x%d=%f\t",i+1,xo[i]);

}

printf("Enter the allowed error:");

scanf("%f",&e);

do{

for(i=0;i<n;i++)

{

sum=b[i];

for(j=0;j<n;j++)

{

if(j!=i)

sum=sum-a[i][j]*xo[j];

}

x1[i]=sum/a[i][i];

if(fabs(x1[i]-xo[i])<e)

{

      key=key+1;

      xo[i]=x1[i];

}

}

}while(key<n);

           

}

if(key==n)

   for(i=0;i<n;i++)

     printf("%f\t",xo[i]);

}

Answer 1

instead of using gauss jacobi use gauss siedel method to correct.

because ur code has multiple bugs i have an alternative way to solve ur code without siedel method.

#include<stdio.h>
#include<stdlib.h>
#include<math.h>

int main() {
    int a[5][5], b[5], n, i, j, flag = 1;
    float e, sum, x[10], old_x, max_error, s;
    
    setbuf(stdout, NULL);
    printf("This program illustrates Gauss Seidel Method in C :\n");
    printf("Enter the dimension of the coefficient matrix A: ");
    scanf("%d", &n);
    
    printf("Enter the %d elements of the coefficient matrix A:\n", n*n);
    for(i=0; i<n; i++) {
        for(j=0; j<n; j++) {
            scanf("%d", &a[i][j]);
        }
    }
        
    printf("Enter the elements of the constant matrix B: ");
    for(i=0; i<n; i++) {
        scanf("%d", &b[i]);
    }
        
    printf("\nThe given system of linear equations is:\n");
    for(i=0; i<n; i++) {
        for(j=0; j<n; j++) {
            printf("%dx%d", a[i][j], j+1);
            if(j < n-1) printf(" + ");
            else printf(" = ");
        }
        printf("%d\n", b[i]);
    }
    
    // Diagonal Dominance check
    for(i=0; i<n; i++) {
        s = 0;
        for(j=0; j<n; j++) {
            if(i != j) s = s + fabs(a[i][j]);
        }
        if(fabs(a[i][i]) < s) {
            flag = 0;
            break;
        }
    }
    
    if(flag == 0) {
        printf("\nError! The given system of linear equations is not diagonally dominant.\n");
        exit(0);
    }
    
    printf("\nThe given system of linear equations is diagonally dominant.\n");
    printf("Enter the initial approximate solution to the given system:\n");
    for(i=0; i<n; i++) {
        printf("x%d: ", i+1);
        scanf("%f", &x[i]);
    }
    
    printf("Enter the allowed error: ");
    scanf("%f", &e);
    
    int iterations = 0;
    do {
        max_error = 0; // Tracks the largest change among all variables this iteration
        
        for(i=0; i<n; i++) {
            old_x = x[i]; // Store the previous value of this specific variable
            sum = b[i];
            
            for(j=0; j<n; j++) {
                if(j != i) {
                    // Gauss-Seidel change: x[j] always contains the newest calculated value
                    sum = sum - a[i][j] * x[j];
                }
            }
            x[i] = sum / a[i][i]; // Instantly update the array
            
            // Check if the change for this specific variable is the largest so far
            float current_error = fabs(x[i] - old_x);
            if(current_error > max_error) {
                max_error = current_error;
            }
        }
        
        iterations++;
        if(iterations > 1000) { // Safety guard against infinite loops
            printf("\nSolution did not converge within 1000 iterations.\n");
            exit(0);
        }
        
    } while(max_error > e); // Loop until the worst-case error falls below threshold
    
    printf("\nThe final solution after %d iterations is:\n", iterations);
    for(i=0; i<n; i++) {
        printf("x%d = %f\n", i+1, x[i]);
    }
    
    return 0;
}

This is gauss siedel method