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2014.59: Generalized rational Krylov decompositions with an application to rational approximation

2014.59: Mario Berljafa and Stefan Güttel (2014) Generalized rational Krylov decompositions with an application to rational approximation.

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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 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 30 Functions of a complex variable
MSC 2000 > 65 Numerical analysis
MIMS number:2014.59
Deposited By:Stefan Güttel
Deposited On:31 March 2015

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