Generalized rational Krylov decompositions with an application to rational approximation

Berljafa, Mario and Güttel, Stefan (2014) Generalized rational Krylov decompositions with an application to rational approximation. [MIMS Preprint]

Warning
There is a more recent version of this item available.
[thumbnail of main.pdf] PDF
main.pdf
Download (1MB)

Abstract

Generalized rational Krylov decompositions are matrix relations which, under certain conditions, are associated with rational Krylov spaces. We study the algebraic properties of such decompositions and present an implicit Q theorem for rational Krylov spaces. Transformations on rational Krylov decompositions allow for changing the poles of a rational Krylov space without recomputation, and two algorithms are presented for this task. Using such transformations we develop a rational Krylov method for rational least squares fitting. Numerical experiments indicate that the proposed method converges fast and robustly. A MATLAB toolbox with implementations of the presented algorithms and experiments is provided.

Item Type: MIMS Preprint
Additional Information: All algorithms and numerical experiments presented in this paper are contained in a MATLAB toolbox available for download from http://guettel.com/rktoolbox
Uncontrolled Keywords: rational Krylov decomposition, inverse eigenvalue problem, rational approximation
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 30 Functions of a complex variable
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 28 Nov 2014
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2198

Available Versions of this Item

Actions (login required)

View Item View Item