On perturbation bounds of Kronecker product linear systems and their level-2 condition numbers

Hua Xiang; Huaian Diao; Yimin Wei

doi:10.1016/j.cam.2005.01.014

On perturbation bounds of Kronecker product linear systems and their level-2 condition numbers

Hua Xiang
, Huaian Diao
, Yimin Wei

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

7 Citations (Scopus)

Abstract

The classical perturbation theory of linear systems Ax = b is extended to Kronecker product linear systems (A ⊗ B) x = d. Upper bounds are derived for the normwise and componentwise condition number. The nearness to singularity and the sensitivity of the condition numbers are analyzed. © 2005 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	210-231
Journal	Journal of Computational and Applied Mathematics
Volume	183
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2005.01.014
Publication status	Published - 1 Nov 2005

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

This work is supported by NSFC (No. 10471027) and Shanghai Education Committee.

Research Keywords

Backward error
Componentwise
Condition number
Kronecker product
Normwise
Perturbation
Sensitivity

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abstract = "The classical perturbation theory of linear systems Ax = b is extended to Kronecker product linear systems (A ⊗ B) x = d. Upper bounds are derived for the normwise and componentwise condition number. The nearness to singularity and the sensitivity of the condition numbers are analyzed. {\textcopyright} 2005 Elsevier B.V. All rights reserved.",

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AU - Xiang, Hua

AU - Diao, Huaian

AU - Wei, Yimin

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - The classical perturbation theory of linear systems Ax = b is extended to Kronecker product linear systems (A ⊗ B) x = d. Upper bounds are derived for the normwise and componentwise condition number. The nearness to singularity and the sensitivity of the condition numbers are analyzed. © 2005 Elsevier B.V. All rights reserved.

AB - The classical perturbation theory of linear systems Ax = b is extended to Kronecker product linear systems (A ⊗ B) x = d. Upper bounds are derived for the normwise and componentwise condition number. The nearness to singularity and the sensitivity of the condition numbers are analyzed. © 2005 Elsevier B.V. All rights reserved.

KW - Backward error

KW - Componentwise

KW - Condition number

KW - Kronecker product

KW - Normwise

KW - Perturbation

KW - Sensitivity

UR - https://www.scopus.com/pages/publications/22144466601

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-22144466601&origin=recordpage

U2 - 10.1016/j.cam.2005.01.014

DO - 10.1016/j.cam.2005.01.014

M3 - RGC 21 - Publication in refereed journal

SN - 0377-0427

VL - 183

SP - 210

EP - 231

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

On perturbation bounds of Kronecker product linear systems and their level-2 condition numbers

Abstract

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Research Keywords

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