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