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A Riemannian inexact Newton-CG method for constructing a nonnegative matrix with prescribed realizable spectrum
Zhao, Zhi1; Bai, Zheng-Jian2; Jin, Xiao-Qing3
2018-12
Source PublicationNUMERISCHE MATHEMATIK
ISSN0029-599X
Volume140Issue:4Pages:827-855
Abstract

This paper is concerned with the inverse eigenvalue problem of finding a nonnegative matrix such that it has the prescribed realizable spectrum. We reformulate the inverse eigenvalue problem as an under-determined constrained nonlinear matrix equation over several matrix manifolds. Then we propose a Riemannian inexact Newton-CG method for solving the nonlinear matrix equation. The global and quadratic convergence of the proposed method is established under some assumptions. We also extend the proposed method to the case of prescribed entries. Finally, numerical experiments are reported to illustrate the efficiency of the proposed method.

DOI10.1007/s00211-018-0982-2
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000447395500001
PublisherSPRINGER HEIDELBERG
The Source to ArticleWOS
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Citation statistics
Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Mathematics,School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, People’s Republic of China
2.School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen 361005, People’s Republic of China
3.Department of Mathematics, University of Macau, Macao, People’s Republic of China
Recommended Citation
GB/T 7714
Zhao, Zhi,Bai, Zheng-Jian,Jin, Xiao-Qing. A Riemannian inexact Newton-CG method for constructing a nonnegative matrix with prescribed realizable spectrum[J]. NUMERISCHE MATHEMATIK,2018,140(4):827-855.
APA Zhao, Zhi,Bai, Zheng-Jian,&Jin, Xiao-Qing.(2018).A Riemannian inexact Newton-CG method for constructing a nonnegative matrix with prescribed realizable spectrum.NUMERISCHE MATHEMATIK,140(4),827-855.
MLA Zhao, Zhi,et al."A Riemannian inexact Newton-CG method for constructing a nonnegative matrix with prescribed realizable spectrum".NUMERISCHE MATHEMATIK 140.4(2018):827-855.
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