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Numerical Linear Algebra

Overview

This repository contains implementations of key numerical methods related to matrix computations. These methods were developed as part of the SF2524 Matrix Computations for Large-scale Systems course at KTH Royal Institute of Technology.

Implemented Methods

The repository includes the following Julia implementations:

  • Arnoldi Iteration (arnoldi.jl, arnoldi2.jl, direct_arnoldi.jl): Algorithms for generating Krylov subspaces and approximating eigenvalues of large matrices.
  • Power Method (power_method.jl): A simple iterative algorithm for finding the dominant eigenvalue and eigenvector of a matrix.
  • Rayleigh Quotient Iteration (rayleigh_quotient.jl): An advanced method for eigenvalue computation that converges rapidly near an eigenvalue.
  • Bwedgemat (Bwedge.mat): A sample matrix used for testing and demonstrating the algorithms.

How to Use

  1. Clone the Repository:

    git clone https://github.com/safa0rhan/NumericalLinearAlgebra.git
cd NumericalLinearAlgebra

  2. Run Julia Scripts: Ensure Julia is installed on your system. Then, execute any of the scripts:

    julia arnoldi.jl

Prerequisites

  • Julia: Ensure that Julia is installed. You can download it from Julia's official website.
  • Any additional dependencies are specified in the scripts and can be added using Julia's package manager.