Bounds for singular values based on the eigenvectors

Nir Cohen; Izchak Lewkowicz

doi:10.1016/0024-3795(91)90336-U

Bounds for singular values based on the eigenvectors

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

Abstract

For a nondefective matrix A ∈ C^n×n, the known inequalities |λ_k|/χ \ ̌ σ_k \ ̌ |λ_k|χ express a bound on the possible ratio between the kth singular value σ_k of A and its kth eigenvalue λ_k, based only on the condition number χ of the associated eigenvector matrix. We obtain and analyse several refinements to this bound.

Original language	English
Pages (from-to)	227-248
Number of pages	22
Journal	Linear Algebra and Its Applications
Volume	149
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(91)90336-U
State	Published - 15 Apr 1991
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(91)90336-U

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title = "Bounds for singular values based on the eigenvectors",

abstract = "For a nondefective matrix A ∈ Cn×n, the known inequalities |λk|/χ \{\v } σk \{\v } |λk|χ express a bound on the possible ratio between the kth singular value σk of A and its kth eigenvalue λk, based only on the condition number χ of the associated eigenvector matrix. We obtain and analyse several refinements to this bound.",

author = "Nir Cohen and Izchak Lewkowicz",

year = "1991",

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doi = "10.1016/0024-3795(91)90336-U",

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journal = "Linear Algebra and Its Applications",

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AU - Cohen, Nir

AU - Lewkowicz, Izchak

PY - 1991/4/15

Y1 - 1991/4/15

N2 - For a nondefective matrix A ∈ Cn×n, the known inequalities |λk|/χ \ ̌ σk \ ̌ |λk|χ express a bound on the possible ratio between the kth singular value σk of A and its kth eigenvalue λk, based only on the condition number χ of the associated eigenvector matrix. We obtain and analyse several refinements to this bound.

AB - For a nondefective matrix A ∈ Cn×n, the known inequalities |λk|/χ \ ̌ σk \ ̌ |λk|χ express a bound on the possible ratio between the kth singular value σk of A and its kth eigenvalue λk, based only on the condition number χ of the associated eigenvector matrix. We obtain and analyse several refinements to this bound.

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U2 - 10.1016/0024-3795(91)90336-U

DO - 10.1016/0024-3795(91)90336-U

M3 - Article

AN - SCOPUS:44949275672

SN - 0024-3795

VL - 149

SP - 227

EP - 248

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Bounds for singular values based on the eigenvectors

Abstract

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