Eigenvalue inclusion regions from inverses of shifted matrices

M.E. Hochstenbach; D.A. Singer; P.F. Zachlin

doi:10.1016/j.laa.2008.08.016

Eigenvalue inclusion regions from inverses of shifted matrices

M.E. Hochstenbach
, D.A. Singer
, P.F. Zachlin

Scientific Computing

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

Abstract

We consider eigenvalue inclusion regions based on the field of values, pseudospectra, Gershgorin region, and Brauer region of the inverse of a shifted matrix. A family of these inclusion regions is derived by varying the shift. We study several properties, one of which is that the intersection of a family is exactly the spectrum. The numerical approximation of the inclusion sets for large matrices is also examined.

Original language	English
Pages (from-to)	2481-2496
Journal	Linear Algebra and Its Applications
Volume	429
Issue number	10
DOIs	https://doi.org/10.1016/j.laa.2008.08.016
Publication status	Published - 2008

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10.1016/j.laa.2008.08.016

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title = "Eigenvalue inclusion regions from inverses of shifted matrices",

abstract = "We consider eigenvalue inclusion regions based on the field of values, pseudospectra, Gershgorin region, and Brauer region of the inverse of a shifted matrix. A family of these inclusion regions is derived by varying the shift. We study several properties, one of which is that the intersection of a family is exactly the spectrum. The numerical approximation of the inclusion sets for large matrices is also examined.",

author = "M.E. Hochstenbach and D.A. Singer and P.F. Zachlin",

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T1 - Eigenvalue inclusion regions from inverses of shifted matrices

AU - Hochstenbach, M.E.

AU - Singer, D.A.

AU - Zachlin, P.F.

PY - 2008

Y1 - 2008

N2 - We consider eigenvalue inclusion regions based on the field of values, pseudospectra, Gershgorin region, and Brauer region of the inverse of a shifted matrix. A family of these inclusion regions is derived by varying the shift. We study several properties, one of which is that the intersection of a family is exactly the spectrum. The numerical approximation of the inclusion sets for large matrices is also examined.

AB - We consider eigenvalue inclusion regions based on the field of values, pseudospectra, Gershgorin region, and Brauer region of the inverse of a shifted matrix. A family of these inclusion regions is derived by varying the shift. We study several properties, one of which is that the intersection of a family is exactly the spectrum. The numerical approximation of the inclusion sets for large matrices is also examined.

U2 - 10.1016/j.laa.2008.08.016

DO - 10.1016/j.laa.2008.08.016

M3 - Article

SN - 0024-3795

VL - 429

SP - 2481

EP - 2496

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 10

ER -

Eigenvalue inclusion regions from inverses of shifted matrices

Abstract

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