Math Department (Thesis/2008-09)

Dynamics of Iterative Eigenvalue Methods

Under the direction of: Jue Wang

---

Large-scale eigenvalue problems often arise in the stability analysis of various applications. Arnold's method is used to compute a few eigenvalues and eigenvectors of large, sparse matrices efficiently. It uses orthogonal matrix transformations to reduce the full Jacobian matrix to a much smaller upper Hessenberg form, whose eigenvalues can be computed with very little computational effort. We will investigate and understand the dynamics of this process, and compare the convergence of the Power method, QR algorithm, Rayleigh Quotient Iteration, and Arnold's method.

Students need to have some knowledge on linear algebra, and need to know (or will have to learn) some techniques on numerical analysis and programming in Matlab.

This topic is suitable for a one-term thesis.

Math Department web pages Created: 01 Apr 2005 Last modified: 24 Apr 2008 15:48:56 Comments to: math@union.edu

Thesis Topics - J. Wang Thesis Topics for 2008-2009 Thesis Topics - C. Tonnesen-Friedman