Comparison of Stationary and Non-Stationary Iterative Methods

This project implements and compares stationary and non-stationary iterative methods for solving large sparse linear systems. The implemented methods are:

• Jacobi Method (Stationary)
• Gauss-Seidel Method (Stationary)
• Conjugate Gradient (CG) Method (Non-Stationary)
• Generalized Minimal Residual (GMRES) Method (Non-Stationary)

The implementation is written in C++, utilizing the Eigen library for basic matrix operations and functionalities.

Features

• Implementation of stationary and non-stationary iterative solvers.
• Comparative analysis of performance metrics:
  • Convergence speed.
  • Accuracy of solutions.
  • Computational efficiency.
• Designed to handle large sparse matrices.

Prerequisites

To run this project, ensure the following are installed on your system:

1. C++ Compiler (e.g., g++, clang++)
2. CMake (For building the project)
3. Eigen (Matrix library)

Building and Running

Clone the Repository

git clone https://github.com/weebsuryansh/IterativeMethods
cd IterativeMethods

Build the project

mkdir build
cd build
cmake ..
make

Running the executable

.\IterativeMethods

Input format

The code uses 3x3, 4x4, 5x5 and 6x6 matrices that can be edited by going into the \data directory.
The matrices used are in .mtx format.

Result and Analysis

Result and analysis can be found in Iterative_Methods.pdf.

Project Structure

IterativeMethods/ 
├── CMakeLists.txt          # Build configuration
├── Eigen/                  # Library used for basic matrix operations 
├── data/                   # Example input files (matrices and vectors) 
├── build/                  # Directory for compiled files (generated) 
├── Iterative_Methods.pdf   # The research paper entailing the result and analysis 
└── README.md               # Project documentation