Alternating direction implicit iteration solution of Lyapunov equations

Author

An Lu

Date of Award

8-1990

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

E. L. Wachspress

Abstract

In this thesis, a new procedure is presented for solving the Lyapunov equations. First, the system is reduced to tridiagonal form with Gaussian similarity transformations, then the resulting system is solved with Alternating-Direction-Implicit (ADI) iteration. A matrix commutation property essential for "model problem" convergence of ADI iteration applied to elliptic difference equations is not needed for this application. All stable Lyapunov matrix equations are model ADI problems.

Recommended Citation

Lu, An, "Alternating direction implicit iteration solution of Lyapunov equations. " Master's Thesis, University of Tennessee, 1990.
https://trace.tennessee.edu/utk_gradthes/12713