README.md

Project 2: Computing Eigenvalues and Eigenvectors using Normalized Power Iteration together with Deflation

Introduction

This project involves the implementation of the normalized power iteration algorithm in combination with deflation to find two eigenvalues and the corresponding eigenvector for the dominant eigenvalue of a square matrix, A.

The program is implemented in C/C++, emphasizing on good programming style and the use of Object Oriented Programming concepts.

How to Compile and Run

1. Compile the C++ Program: Navigate to the directory containing source.cpp and compile the code by running:

   g++ -o source source.cpp
   

2. Execute the Program: Run the compiled program with the command:

   ./source A.txt 1e-6 output.txt
   

   where,
   • A.txt is the input file containing the square matrix A,
   • 1e-6 is the tolerance for the power iteration algorithm,
   • output.txt is the output file where the eigenvalues and corresponding eigenvectors are written.

Programming Details

The program:

• Accepts three command-line arguments representing the input file, tolerance, and output file.
• Uses dynamically allocated memory to store the matrix.
• Prints an error message and exits upon detecting any problems.
• Calculates the eigenvalues and corresponding eigenvectors and writes them to a text file.

About the OOP Approach

In this project, matrix operations are performed using a Matrix class, with operations such as multiplication, addition, and transposition implemented as methods of this class. This approach eliminates the need for complex loops in the program.

Contents

• ProjectDescription: Project Description for details.
• source.cpp: This is the primary program file written in C++.
• readme.txt: This file includes instructions for compiling and running the program.
• A.txt: is a n x n square matrix.
• output.txt: A's dominant eigenvalue, its corresponding eigenvector and the next eigenvalue.