Solving singular generalized eigenvalue problems by a rank-completing perturbation

Michiel E. Hochstenbach; Christian Mehl; Bor Plestenjak

doi:10.1137/18M1188628

Solving singular generalized eigenvalue problems by a rank-completing perturbation

Michiel E. Hochstenbach
, Christian Mehl
, Bor Plestenjak

Center for Analysis, Scientific Computing and Applications

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

23 Citaten (Scopus)

76 Downloads (Pure)

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Generalized eigenvalue problems involving a singular pencil are very challenging to solve, with respect to both accuracy and efficiency. The existing package Guptri is very elegant but may be time-demanding, even for small and medium-sized matrices. We propose a simple method to compute the eigenvalues of singular pencils, based on one perturbation of the original problem of a certain specific rank. For many problems, the method is both fast and robust. This approach may be seen as a welcome alternative to staircase methods.

Originele taal-2	Engels
Pagina's (van-tot)	1022-1046
Aantal pagina's	25
Tijdschrift	SIAM Journal on Matrix Analysis and Applications
Volume	40
Nummer van het tijdschrift	3
DOI's	https://doi.org/10.1137/18M1188628
Status	Gepubliceerd - 5 sep. 2019

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∗Received by the editors May 21, 2018; accepted for publication (in revised form) by K. Meerbergen June 5, 2019; published electronically September 5, 2019. https://doi.org/10.1137/18M1188628 Funding: The work of the first author was supported by an NWO Vidi research grant. The work of the second author was supported by a Dutch 4TU AMI visitor’s grant. The work of the third author was partially supported by Slovenian Research Agency grant P1-0294. †Department of Mathematics and Computer Science, TU Eindhoven, Eindhoven, 5600 MB, Netherlands ([email protected]). ‡Institut für Mathematik, Technische Universität Berlin, Sekretariat MA 4-5, 10623 Berlin, Germany ([email protected]). §Department of Mathematics, University of Ljubljana, Ljubljana, 1000, Slovenia ([email protected]).

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abstract = "Generalized eigenvalue problems involving a singular pencil are very challenging to solve, with respect to both accuracy and efficiency. The existing package Guptri is very elegant but may be time-demanding, even for small and medium-sized matrices. We propose a simple method to compute the eigenvalues of singular pencils, based on one perturbation of the original problem of a certain specific rank. For many problems, the method is both fast and robust. This approach may be seen as a welcome alternative to staircase methods.",

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Solving singular generalized eigenvalue problems by a rank-completing perturbation

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