This is a C++ Program to implement Gauss Seidel Method. In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations.

Here is source code of the C++ Program to Implement Gauss Seidel Method. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

`#include<iostream>`

`#include<conio.h>`

using namespace std;

int main(void)

`{`

float a[10][10], b[10], x[10], y[10];

int n = 0, m = 0, i = 0, j = 0;

cout << "Enter size of 2d array(Square matrix) : ";

cin >> n;

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

`{`

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

`{`

cout << "Enter values no :(" << i << ", " << j << ") ";

cin >> a[i][j];

`}`

`}`

cout << "\nEnter Values to the right side of equation\n";

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

`{`

cout << "Enter values no :(" << i << ", " << j << ") ";

cin >> b[i];

`}`

cout << "Enter initial values of x\n";

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

`{`

cout << "Enter values no. :(" << i<<"):";

cin >> x[i];

`}`

cout << "\nEnter the no. of iteration : ";

cin >> m;

while (m > 0)

`{`

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

`{`

y[i] = (b[i] / a[i][i]);

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

`{`

if (j == i)

continue;

y[i] = y[i] - ((a[i][j] / a[i][i]) * x[j]);

x[i] = y[i];

`}`

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

`}`

cout << "\n";

m--;

`}`

return 0;

`}`

Output:

$ g++ GaussSeidel.cpp $ a.out Enter size of 2d array(Square matrix) : 3 Enter values no :(0, 0) 2 Enter values no :(0, 1) 3 Enter values no :(0, 2) 1 Enter values no :(1, 0) 5 Enter values no :(1, 1) 4 Enter values no :(1, 2) 6 Enter values no :(2, 0) 8 Enter values no :(2, 1) 7 Enter values no :(2, 2) 9 Enter Values to the right side of equation Enter values no :(0, 3) 2 Enter values no :(1, 3) 3 Enter values no :(2, 3) 4 Enter initial values of x Enter values no. :(0): 0 Enter values no. :(1): 0 Enter values no. :(2): 0 Enter the no. of iteration : 4 x1 = 1.000000 x2 = -0.500000 x3 = -0.055556 x1 = 1.777778 x2 = -1.388889 x3 = -0.055556 x1 = 3.111111 x2 = -3.055555 x3 = 0.055555 x1 = 5.555555 x2 = -6.277777 x3 = 0.388889

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