Linear system based approach for solving some related problems of M-matrices

Jin Liang Shao; Ting Zhu Huang; Guofeng Zhang

doi:10.1016/j.laa.2009.08.011

Linear system based approach for solving some related problems of M-matrices

Jin Liang Shao
, Ting Zhu Huang
, Guofeng Zhang

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

Abstract

This paper develops a novel linear system based approach for computing {norm of matrix} A- 1{norm of matrix}∞, the Skeel condition number of an M-matrix A, and the positive diagonal matrices D guaranteeing that AD be a strictly diagonally dominant matrix. Theoretic analysis and simulation results justify the validity of the proposed approach. Moreover, the proposed linear system model can be implemented by application-specific integrated circuits, and then it has asynchronous parallel processing ability and can achieve high computing performance.

Original language	English
Pages (from-to)	327-337
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	432
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2009.08.011
Publication status	Published - 1 Jan 2010
Externally published	Yes

Keywords

Diagonal dominance
Infinity norm
Linear system
M-matrix
Skeel condition number

ASJC Scopus subject areas

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

More information

10.1016/j.laa.2009.08.011

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abstract = "This paper develops a novel linear system based approach for computing \{norm of matrix\} A- 1\{norm of matrix\}∞, the Skeel condition number of an M-matrix A, and the positive diagonal matrices D guaranteeing that AD be a strictly diagonally dominant matrix. Theoretic analysis and simulation results justify the validity of the proposed approach. Moreover, the proposed linear system model can be implemented by application-specific integrated circuits, and then it has asynchronous parallel processing ability and can achieve high computing performance.",

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AB - This paper develops a novel linear system based approach for computing {norm of matrix} A- 1{norm of matrix}∞, the Skeel condition number of an M-matrix A, and the positive diagonal matrices D guaranteeing that AD be a strictly diagonally dominant matrix. Theoretic analysis and simulation results justify the validity of the proposed approach. Moreover, the proposed linear system model can be implemented by application-specific integrated circuits, and then it has asynchronous parallel processing ability and can achieve high computing performance.

KW - Diagonal dominance

KW - Infinity norm

KW - Linear system

KW - M-matrix

KW - Skeel condition number

UR - https://www.scopus.com/pages/publications/70449532199

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Linear system based approach for solving some related problems of M-matrices

Abstract

Keywords

ASJC Scopus subject areas

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