Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix

Moshe Haviv; Yakov Ritov; Uriel G. Rothblum

doi:10.1016/0024-3795(87)90158-3

Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix

Moshe Haviv^*
, Yakov Ritov
, Uriel G. Rothblum

^*Corresponding author for this work

Department of Statistics

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

7 Scopus citations

Abstract

Two easily computable sequences of bounds on the subdominant modulus of an eigenvalue of a square nonnegative matrix are obtained. In particular it is shown that the sequences converge to the subdominant modulus. A sequence of bounds generated by a method of Brauer (1971) turns out to be a subsequence of one of our sequences. Thus, our results imply the convergence of Brauer's sequence.

Original language	English
Pages (from-to)	61-75
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	87
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(87)90158-3
State	Published - Mar 1987

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title = "Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix",

abstract = "Two easily computable sequences of bounds on the subdominant modulus of an eigenvalue of a square nonnegative matrix are obtained. In particular it is shown that the sequences converge to the subdominant modulus. A sequence of bounds generated by a method of Brauer (1971) turns out to be a subsequence of one of our sequences. Thus, our results imply the convergence of Brauer's sequence.",

author = "Moshe Haviv and Yakov Ritov and Rothblum, \{Uriel G.\}",

year = "1987",

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AU - Haviv, Moshe

AU - Ritov, Yakov

AU - Rothblum, Uriel G.

PY - 1987/3

Y1 - 1987/3

N2 - Two easily computable sequences of bounds on the subdominant modulus of an eigenvalue of a square nonnegative matrix are obtained. In particular it is shown that the sequences converge to the subdominant modulus. A sequence of bounds generated by a method of Brauer (1971) turns out to be a subsequence of one of our sequences. Thus, our results imply the convergence of Brauer's sequence.

AB - Two easily computable sequences of bounds on the subdominant modulus of an eigenvalue of a square nonnegative matrix are obtained. In particular it is shown that the sequences converge to the subdominant modulus. A sequence of bounds generated by a method of Brauer (1971) turns out to be a subsequence of one of our sequences. Thus, our results imply the convergence of Brauer's sequence.

UR - https://www.scopus.com/pages/publications/38249038424

U2 - 10.1016/0024-3795(87)90158-3

DO - 10.1016/0024-3795(87)90158-3

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AN - SCOPUS:38249038424

SN - 0024-3795

VL - 87

SP - 61

EP - 75

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix

Abstract

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