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# Numerical Methods: Gauss Seidel

03.24.2012
| 1657 views |
```        This solves systems of equations using the Gauss Seidel Method.

```
```/*
* File:   main.cpp
* Author: Bangonkali
*
* Created on March 23, 2012, 8:14 PM
*/
#include <iostream>
#include <cmath>
#include <cstdlib>

// example taken from wikipedia
// http://j.mp/GV1mPz

using namespace std;

void printMatrix(int N, double A[20][21]) {
for (int i = 0; i < N; i++)
{
for (int j = 0; j <= N; j++)
{
cout << A[i][j] << '\t';
}

cout << endl;
}

cout << endl;
}

int gauss_seidel(int N, double A [20] [21], double r[20], double error[20]) {
double r_old[N-1];

for (int i = 0; i < N; i++) {
r[i] = 0; // make initial guess to 0
r_old[i] = 0; // make initial guess to 0
error[i] = 0; // make all errors to 0
}

double max_absolute_error = 0;
int iter = 0;
for (iter = 0; iter < 1E12; iter++) {
// get each iteration result
max_absolute_error = 0;
for (int i = 0; i < N; i++) {
r_old[i] = r[i];
r[i] = A[i][N] / A[i][i];
for (int j = 0; j < N; j++) {
if (j == i ) continue;
r[i] = r[i] - (A[i][j] * r[j]) / A[i][i];
}

error[i] = abs((r[i] - r_old[i]) / r[i]) * 100;
if (error[i] > max_absolute_error) {
max_absolute_error = error[i];

}
}
//        for (int i=0; i<3; i++) cout << r[i] << "  ";
//        cout << "max_absolute_error = " << max_absolute_error << endl;
if (max_absolute_error < 1E-12) {
cout << "error break" << endl;
return iter;
}
}

return iter;
}
/*
*
*/
int main(int argc, char** argv) {
double A[20][21];
double X[20];
double E[20];

bool err;

A[0][0] = 7;
A[0][1] = -2;
A[0][2] = 1;
A[0][3] = 2;
A[0][4] = 3;

A[1][0] = 2;
A[1][1] = 8;
A[1][2] = 3;
A[1][3] = 1;
A[1][4] = -2;

A[2][0] = -1;
A[2][1] = 0;
A[2][2] = 5;
A[2][3] = 2;
A[2][4] = 5;

A[3][0] = 0;
A[3][1] = 2;
A[3][2] = -1;
A[3][3] = 4;
A[3][4] = 4;

printMatrix(4,A);
int iterations = gauss_seidel(4, A, X, E);
for (int i=0; i<3; i++) cout << X[i] << "  ";
cout << endl;
for (int i=0; i<3; i++) cout << E[i] << "  ";
cout << endl;
cout << "iterations = " << iterations << endl;
return 0;
}

```
`    `
"Starting from scratch" is seductive but disease ridden