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Bisection forAx=λBx with matrices of variable band width

Bisektion fürAx=λBx mit Matrizen mit variabler Bandbreite

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Abstract

Some extensions of the bisection method and of the inverse vector iteration for the general eigenvalue problemAx=λBx with symmetric matrices are given. A version with restricted pivoting is applied to sparse matricesA andB in which case the decomposition ofA-μB can be performed within an extended envelope with respect to the envelopeA andB. The effect of these refinements is illustrated by an example.

Zusammenfassung

Es werden einige Ergänzungen zur Bisektionsmethode mit anschließender inverser Vektoriteration für das allgemeine EigenwertproblemAx=λBx mit symmetrischen Matrizen gemacht. Eine Version mit beschränkter Pivotsuche wird auf schwach besetzte MatrizenA undB angewendet, wobei die Zerlegung vonA-μB in einer, gegenüber der Hülle vonA undB, leicht erweiterten Hülle abläuft. Der Effekt dieser Verbesserungen wird an einem Beispiel illustriert.

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References

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Authors and Affiliations

  1. Seminar für Angewandte Mathematik, Universität Zürich, Freiestrasse 36, CH-8032, Zürich, Switzerland

    P. Waldvogel

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  1. P. Waldvogel
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Waldvogel, P. Bisection forAx=λBx with matrices of variable band width. Computing 28, 171–180 (1982). https://doi.org/10.1007/BF02241821

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  • DOI: https://doi.org/10.1007/BF02241821

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