rafa3lp/gausianelimination

Implementation of Gausian elimination for solving linear systems

Gausian Elimination

This is a C program that solves a system of linear equations using Gaussian Elimination. Work carried out as part of the numerical algorithms discipline.

Summary

• Overview
• Usage
• File Format
• Compilation
• Debugging

Overview

This program implements the Gaussian Elimination algorithm to solve a system of linear equations in the form of Ax = b, where A is a square matrix, x is the solution vector, and b is the right-hand side vector.

Usage

1. Create an input file containing the linear system you want to solve.
2. Run the program, passing the input file as a command-line argument.

./gausianElimination linearSystem.dat

File Format

The input file should follow the format described below:

1. The first line should contain a single integer n, representing the dimension of the square matrix A.
2. The next n lines should contain n space-separated values, representing the elements of the matrix A.
3. The final line should contain n space-separated values, representing the elements of the vector b.

Example input file:

3
5.0 2.0 1.0
2.0 -1.0 3.0
0.0 1.0 -2.0
8.0 9.0 -6.0

The file above represents the following linear system:

$$\begin{cases} 5x + 2y + z = 8 \\\ 2x - y + 3z = 9 \\\ y - 2z = -6 \end{cases}$$

Compilation

Use make to compile the program:

make release

Debugging

It is also possible to generate a debug version that better describes the steps performed:

make debug