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## The QR Algorithm for Eigenvalue Estimation: Theory and Experiments

##### Date

2008-12-15##### Author

Feng, Wei

##### Type of Degree

Thesis##### Department

Mathematics and Statistics##### Metadata

Show full item record##### Abstract

In this thesis, we explore one of the most important numerical algorithms ever invented,
the QR algorithm for computing matrix eigenvalues. First, we describe out notations and
mathematical symbols used throughout the thesis in Chapter 1. Then we lay the ground
work by stating and proving some basic lemmas in Chapter 2. Then in Chapter 3, we prove
the convergence of the QR algorithm under the assumption of distinct magnitudes for all
eigenvalues. This constraint is relaxed in Chapter 4, where we prove the convergence of
the QR algorithm under the assumption of possibly equal magnitude eigenvalues. Finally,
in Chapter 5, we present some numerical experiments to validate the conclusions drawn in
this thesis.