Numerical methods for the solution of large and very large, sparse Lyapunov equations

In this dissertation we consider the numerical solution of large $(100 \leq n \leq 1000)$ and very large $(n \geq 1000)$, sparse Lyapunov equations $AX + XA\sp\prime + Q = 0$. We first present a parallel version of the Hammarling algorithm for the solution of Lyapunov equations where the coefficient matrix A is large and dense. We then present a novel parallel algorithm for the solution of Lyapunov equations where A is large and banded. We provide a detailed analysis of the computational requirements in tandem with the results of numerical experiments with these algorithms on an Alliant FX-8 multiprocessor.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Hodel, Alan Scottedward

Contributors dc:contributor

• Poolla, Kameshwar

• Engineering, Electronics and Electrical
• Engineering, Mechanical
• Computer Science

Statement dc:rights

• Copyright 1989 Hodel, Alan Scottedward

Language dc:language

eng

Identifier

AAI9010887
(UMI)AAI9010887

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/19970