Skip to main content
Linear Algebra and Its ApplicationsVolume 565, 15 March 2019, Pages 99-122

An infinity norm bound for the inverse of Dashnic–Zusmanovich type matrices with applications(Article)(Open Access)

  Save all to author list
  • aSchool of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, China
  • bDepartment of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, 21000, Serbia
  • cSchool of Mathematics Sciences, Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China
  • dCollege of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China

Abstract

An upper bound for the infinity norm for the inverse of Dashnic–Zusmanovich type matrices is given. It is proved that the upper bound is sharper than the well-known Varah's bound for strictly diagonally dominant matrices. By introducing a new subclass of P-matrices: Dashnic–Zusmanovich type B-matrices (DZ-type-B-matrices), and using the proposed infinity norm bound, an error bound is given for the linear complementarity problems of DZ-type-B-matrices. We also give a new pseudospectra localization to measure the distance to instability. © 2018 Elsevier Inc.

Author keywords

Dashnic–Zusmanovich type matricesDZ-type-B-matricesH-matricesInfinity normLinear complementarity problemsPseudospectra localization

Indexed keywords

Engineering controlled terms:Inverse problems
Engineering uncontrolled termsError boundH-matricesInfinity normLinear complementarity problemsP-matricesPseudospectraStrictly diagonally dominant matricesUpper Bound
Engineering main heading:Matrix algebra

Funding details

Funding sponsor Funding number Acronym
2018YDJQ021
National Natural Science Foundation of China11501141NSFC
National Natural Science Foundation of ChinaNSFC
Guizhou Science and Technology DepartmentQKHJZ [2015]2073
Guizhou Science and Technology Department
Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja174019MPNTR
Ministarstvo Prosvete, Nauke i Tehnološkog RazvojaMPNTR
Yunnan Provincial Science and Technology Department2018FB001
Yunnan Provincial Science and Technology Department
Department of Education of Guizhou ProvinceQJHKYZ [2016]066
Department of Education of Guizhou Province

  • 1

    The work of Ljiljana Cvetković is supported partly by the Ministry of Education, Science and Technological Development of the Republic of Serbia , Research Grant 174019 .

  • 2

    The work of Chaoqian Li is supported partly by the Applied Basic Research Programs of Yunnan Provincial Science and Technology Department [Grant No. 2018FB001 ], Outstanding Youth Cultivation Project for Yunnan Province [Grant No. 2018YDJQ021 ] and Program for Excellent Young Talents in Yunnan University. Chaoqian Li's work was finished while he was a visiting scholar at Shanghai Key Laboratory of Contemporary Applied Mathematics of Fudan University during 2017 and 2018. He would like to thank Prof. Yaotang Li for his teaching on the occasion of his 60th birthday.

  • 3

    The work of Chaoqian Li is supported partly by the Applied Basic Research Programs of Yunnan Provincial Science and Technology Department [Grant No. 2018FB001], Outstanding Youth Cultivation Project for Yunnan Province [Grant No. 2018YDJQ021] and Program for Excellent Young Talents in Yunnan University. Chaoqian Li's work was finished while he was a visiting scholar at Shanghai Key Laboratory of Contemporary Applied Mathematics of Fudan University during 2017 and 2018. He would like to thank Prof. Yaotang Li for his teaching on the occasion of his 60th birthday.The work of Ljiljana Cvetković is supported partly by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Research Grant 174019.The work of Jianxing Zhao is supported partly by National Natural Science Foundation of China (Grant No. 11501141), Science and Technology Top-notch Talents Support Project of Guizhou Provincial Department of Education (Grant No. QJHKYZ [2016]066), and Science and Technology Foundation of Guizhou Province (Grant No. QKHJZ [2015]2073).

  • 4

    The work of Jianxing Zhao is supported partly by National Natural Science Foundation of China (Grant No. 11501141 ), Science and Technology Top-notch Talents Support Project of Guizhou Provincial Department of Education (Grant No. QJHKYZ [2016]066 ), and Science and Technology Foundation of Guizhou Province (Grant No. QKHJZ [2015]2073 ).

  • ISSN: 00243795
  • CODEN: LAAPA
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1016/j.laa.2018.12.013
  • Document Type: Article
  • Publisher: Elsevier Inc.

  Cvetković, L.; Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, Serbia;
© Copyright 2019 Elsevier B.V., All rights reserved.

Cited by 30 documents

Geng, Y. , Zhu, Y. , Zhang, F.
Infinity Norm Bounds for the Inverse of SDD1-Type Matrices with Applications
(2025) Communications on Applied Mathematics and Computation
Lyu, Z. , Liu, D. , Wang, S.
A note on infinity norm bounds for the inverses of Nekrasov matrices
(2024) Mathematical Methods in the Applied Sciences
Li, Q. , Ran, W. , Wang, F.
Infinity norm bounds for the inverse of generalized SDD2 matrices with applications
(2024) Japan Journal of Industrial and Applied Mathematics
View details of all 30 citations
Inform me when this document is cited in Scopus:
Set citation alert Set citation feed
{"topic":{"name":"Eigenvalue; Complementarity Problem; Matrix (Mathematics)","id":32032,"uri":"Topic/32032","prominencePercentile":52.169388,"prominencePercentileString":"52.169","overallScholarlyOutput":0},"dig":"d75d537740167f8bd080a09ccdf7167bc55cd2c5acfa06e6b971d34c0b3da729"}

SciVal Topic Prominence

Topic:
Prominence percentile: