The QR Method For Eigenvalue Problem

Abstract

First of all thanks to Allah the greatest most merciful, thanks for him for giving power and thoughts to complete this thesis. Second my supervisor DR: Mohsin Hassan Abdullah who helped me to complete this research. I am great full to my teachers in the faculty of libraries supervisor and colleagues. Also thanks to our parents and families for support, and I need to express my gratitude and deep appreciation to all those who helped me . IV ABSTRACT This research is concerned with the QR method which is a powerful and important method for finding approximations for all eigenvalues of a given matrix. It is quite suitable for finding the eigenvalues of a matrix of high dimension. In this study a detailed description of the QR method is given. The method will be applied on a similar upper Hessenberg matrix. Plane rotations are used during the iteration . An algorithm of the QR method with shift is designed to accelerate convergence. Matlab computational environment is used in the