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On parabolic and elliptic spectral dichotomy

Alexander Malyshev 1 Miloud Sadkane 1
1 ALADIN - Algorithms Adapted to Intensive Numerical Computing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : We discuss two spectral dichotomy techniques: one for computing an invariant subspace of a nonsymmetric matrix associated with the eigenvalues inside and outside a given parabola. Another for computing a right deflating subspace of a regular matrix pencil associated with the eigenvalues inside and outside a given ellipse. The techniques use matrices of order twice the order of the original matrices on which the spectral dichotomy by the unit circle and by the imaginary axis apply efficiently. We prove the equivalence between the condition number of the original problems and that of the transformed ones.
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Submitted on : Wednesday, May 24, 2006 - 3:06:12 PM
Last modification on : Friday, February 4, 2022 - 3:17:37 AM
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  • HAL Id : inria-00074343, version 1


Alexander Malyshev, Miloud Sadkane. On parabolic and elliptic spectral dichotomy. [Research Report] RR-2332, INRIA. 1994. ⟨inria-00074343⟩



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