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]

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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: 31 Mar 2015