Approximate solves in Krylov-based modeling methods

Author

Grimme, Eric ; Gallivan, Kyle A. ; De Clippel, Valerie ; Van Dooren, Paul

Author_Institution

Intel Corp., Santa Clara, CA, USA

Volume

4

fYear

1997

fDate

10-12 Dec 1997

Firstpage

3849

Abstract

Rational Krylov methods are potentially one of the most robust and efficient algorithms to compute lower order approximations to linear time invariant dynamical systems that match a specified number of moments of the transfer function at multiple points in the complex plane. The characterization of multipoint rational interpolation in terms of bases of multiple Krylov spaces was developed recently. In this paper, we summarize some results concerning the use of approximate solutions to the linear systems of equations that arise on each step of the method. Such approximations are used to reduce the space and time required to produced the reduced order system

Keywords

approximation theory; interpolation; iterative methods; linear systems; modelling; reduced order systems; transfer functions; Krylov spaces; iterative method; linear time invariant dynamical systems; lower order approximations; matrix factorisation; moment matching; multipoint rational interpolation; rational Krylov methods; reduced order system; transfer function; Computational modeling; Equations; Interpolation; Linear approximation; Linear systems; Physics computing; Reduced order systems; Robustness; Sparse matrices; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1997., Proceedings of the 36th IEEE Conference on

Conference_Location

San Diego, CA

ISSN

0191-2216

Print_ISBN

0-7803-4187-2

Type

conf

DOI

10.1109/CDC.1997.652462

Filename

652462