Least-Squares Approximate Solution of Overdetermined Sylvester Equations

Authors

A. Scottedward Hodel, Auburn University Main Campus
Pradeep Misra, Wright State University - Main CampusFollow

Document Type

Article

Publication Date

4-1997

Abstract

We address the problem of computing a low-rank estimate Y of the solution X of the Lyapunov equation AX + XA' + Q = O without computing the matrix X itself. This problem has applications in both the reduced-order modeling and the control of large dimensional systems as well as in a hybrid algorithm for the rapid numerical solution of the Lyapunov equation via the alternating direction implicit method. While no known methods for low-rank approximate solution provide the two-norm optimal rank k estimate Xk of the exact solution X of the Lyapunov equation, our iterative algorithms provide an effective method for estimating the matrix X(k) by minimizing the error AY + YA'+ Q(F).

Comments

Copyright © 1997, Society for Industrial and Applied Mathematics.

Repository Citation

Hodel, A. S., & Misra, P. (1997). Least-Squares Approximate Solution of Overdetermined Sylvester Equations. SIAM Journal on Matrix Analysis and Applications, 18 (2), 279-290.
https://corescholar.libraries.wright.edu/ee/2

DOI

10.1137/S0895479893252337