Some simple estimates for singular values of a matrix

Liqun Qi

doi:10.1016/0024-3795(84)90117-4

Some simple estimates for singular values of a matrix

Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

54 Citations (Scopus)

Abstract

Some simple estimation theorems for singular values of a rectangular matrix A are given. They only use the elements of A itself, and in some cases they yield better results than does the Gerschgorin theorem applied to A*A. A bound for the condition number of A may be obtained from them. When A is square, a bound is derived which explains why scaling improves the performance of Gauss elimination when row or column norms differ widely in magnitude. Their application to perturbation theory of singular values is also discussed.

Original language	English
Pages (from-to)	105-119
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	56
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(84)90117-4
Publication status	Published - 1 Jan 1984
Externally published	Yes

ASJC Scopus subject areas

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

More information

10.1016/0024-3795(84)90117-4

Cite this

@article{1c06483d39b14972be8d61d4d3cbfcfe,

title = "Some simple estimates for singular values of a matrix",

abstract = "Some simple estimation theorems for singular values of a rectangular matrix A are given. They only use the elements of A itself, and in some cases they yield better results than does the Gerschgorin theorem applied to A*A. A bound for the condition number of A may be obtained from them. When A is square, a bound is derived which explains why scaling improves the performance of Gauss elimination when row or column norms differ widely in magnitude. Their application to perturbation theory of singular values is also discussed.",

author = "Liqun Qi",

year = "1984",

month = jan,

day = "1",

doi = "10.1016/0024-3795(84)90117-4",

language = "English",

volume = "56",

pages = "105--119",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "C",

}

TY - JOUR

T1 - Some simple estimates for singular values of a matrix

AU - Qi, Liqun

PY - 1984/1/1

Y1 - 1984/1/1

N2 - Some simple estimation theorems for singular values of a rectangular matrix A are given. They only use the elements of A itself, and in some cases they yield better results than does the Gerschgorin theorem applied to A*A. A bound for the condition number of A may be obtained from them. When A is square, a bound is derived which explains why scaling improves the performance of Gauss elimination when row or column norms differ widely in magnitude. Their application to perturbation theory of singular values is also discussed.

AB - Some simple estimation theorems for singular values of a rectangular matrix A are given. They only use the elements of A itself, and in some cases they yield better results than does the Gerschgorin theorem applied to A*A. A bound for the condition number of A may be obtained from them. When A is square, a bound is derived which explains why scaling improves the performance of Gauss elimination when row or column norms differ widely in magnitude. Their application to perturbation theory of singular values is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0009350931&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(84)90117-4

DO - 10.1016/0024-3795(84)90117-4

M3 - Journal article

SN - 0024-3795

VL - 56

SP - 105

EP - 119

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Some simple estimates for singular values of a matrix

Abstract

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this