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Granat, RobertKågström, Bo
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Department of Computing ScienceHPC2N (High Performance Computing Centre North)
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BIT Numerical Mathematics
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Computing Periodic Deflating Subspaces Associated with a Specified Set of EigenvaluesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2007 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 47, no 4, p. 763-791Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2007. Vol. 47, no 4, p. 763-791
##### Keywords [en]

generalized product of a K-cyclic matrix pair sequence, generalized periodic real Schur form, eigenvalue reordering, periodic generalized coupled Sylvester equation, K-cyclic equivalence transformation, generalized periodic eigenvalue problem
##### Identifiers

URN: urn:nbn:se:umu:diva-21939DOI: 10.1007/s10543-007-0143-yScopus ID: 2-s2.0-36749021070ISBN: 0006-3835 (print)OAI: oai:DiVA.org:umu-21939DiVA, id: diva2:212196
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##### Note

Granat, R. Kagstroem, B. Kressner, D.Available from: 2009-04-21 Created: 2009-04-21 Last updated: 2023-03-24
##### In thesis

We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular K-cyclic matrix pair sequence (A (k) ,E (k) ). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvester-like equation and constructing K pairs of orthogonal matrices. These pairs define an orthogonal K-cyclic equivalence transformation that swaps adjacent diagonal blocks in the Schur form. An error analysis of this swapping procedure is presented, which extends existing results for reordering eigenvalues in the generalized real Schur form of a regular pair (A,E). Our direct reordering method is used to compute periodic deflating subspace pairs corresponding to a specified set of eigenvalues. This computational task arises in various applications related to discrete-time periodic descriptor systems. Computational experiments confirm the stability and reliability of the presented eigenvalue reordering method.

1. Algorithms and Library Software for Periodic and Parallel Eigenvalue Reordering and Sylvester-Type Matrix Equations with Condition Estimation$(function(){PrimeFaces.cw("OverlayPanel","overlay140959",{id:"formSmash:j_idt741:0:j_idt745",widgetVar:"overlay140959",target:"formSmash:j_idt741:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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