gtironi / numerical_linear_algebra

Linear Algebra Algorithms in Scilab

Introduction

This repository contains implementations of several fundamental linear algebra algorithms in Scilab. These algorithms were developed as part of a course on Numerical Linear Algebra and include detailed reports in PDF format within each respective directory.

Table of Contents

1. Algorithms
   • Gaussian Elimination
   • Jacobi Method
   • Gauss-Seidel Method
   • Power Method
   • Least Squares Method
   • Gram-Schmidt Process
   • Householder Transformation
   • QR Algorithm
   • Power Method
2. Installation
3. Usage
4. Features
5. Dependencies
6. Documentation
7. Contributors
8. License

Algorithms

Gaussian Elimination

Implementation of the Gaussian Elimination method for solving systems of linear equations.

Jacobi Method

Implementation of the Jacobi iterative method for solving systems of linear equations.

Gauss-Seidel Method

Implementation of the Gauss-Seidel iterative method for solving systems of linear equations.

Power Method

Implementation of the Power Method for finding the dominant eigenvalue and corresponding eigenvector of a matrix.

Least Squares Method

Implementation of the Least Squares method for finding the best-fitting solution to over-determined systems of linear equations.

Gram-Schmidt Process

Implementation of the Gram-Schmidt process for orthogonalizing a set of vectors in an inner product space.

Householder Transformation

Implementation of the Householder Transformation for QR decomposition and orthogonalization of matrices.

QR Algorithm

Implementation of the QR Algorithm for eigenvalue decomposition of a matrix.

Installation

To use these algorithms, you need to have Scilab installed on your system. You can download it from the official Scilab website.

Usage

Each algorithm is located in a .sci file. To run an algorithm, open the .sci file in Scilab or execute it:

exec('path_to_algorithm.sci');

Replace path_to_algorithm.sci with the path to the specific .sci file you want to run.

Features

• Linear algebra implementations from scratch in Scilab
• Detailed PDF reports
• Educational resource for understanding numerical problems

Dependencies

• Scilab

Documentation

Each folder contains a PDF report that provides detailed implementation details and example numerical problems (portuguese).

Contributors

• Gustavo Tironi

License

This project is licensed under the MIT License. See the LICENSE file for details.