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Article
Least-Squares Approximate Solution of Overdetermined Sylvester Equations
SIAM Journal on Matrix Analysis and Applications
  • A. Scottedward Hodel, Auburn University Main Campus
  • Pradeep Misra, Wright State University - Main Campus
Document Type
Article
Publication Date
4-1-1997
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.

DOI
10.1137/S0895479893252337
Citation Information
A. Scottedward Hodel and Pradeep Misra. "Least-Squares Approximate Solution of Overdetermined Sylvester Equations" SIAM Journal on Matrix Analysis and Applications Vol. 18 Iss. 2 (1997) p. 279 - 290 ISSN: 0895-4798
Available at: http://works.bepress.com/pradeep_misra/2/