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ON THE SOLVABILITY CONDITION AND NUMERICAL ALGORITHM FOR THE PARAMETERIZED GENERALIZED INVERSE EIGENVALUE PROBLEM
Dai, Hua1; Bai, Zhong-Zhi2; Wei, Ying1
2015
Source PublicationSIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN0895-4798
Volume36Issue:2Pages:707-726
AbstractWe discuss the parameterized generalized inverse eigenvalue problem (PGIEP): For given matrices A(i), B-i is an element of C-nxn (i = 0, 1, ... , n), find complex numbers c(i) is an element of C (i = 1, 2, ... , n) such that the generalized eigenvalue problem (A(0) + Sigma(n)(i=1) c(i)A(i))x = lambda(B-0 + Sigma(n)(i=1) c(i)B(i))x has the prescribed eigenvalues lambda(1), lambda(2), ... , lambda(n). We show that this problem is equivalent to a multiparameter eigenvalue problem if the given eigenvalues lambda(1), lambda(2), ... , lambda(n) are distinct. Applying the theory about the multiparameter eigenvalue problem, we obtain sufficient conditions that guarantee the existence of a solution of the PGIEP. In addition, we propose a smooth LU decomposition for a matrix depending on several parameters and discuss its algebraic property. Based on these theoretical results, we present a numerical algorithm for solving the PGIEP and prove its locally quadratic convergence. Numerical implementations show that the new algorithm is feasible and effective for solving the PGIEP.
Keywordinverse eigenvalue problem multiparameter eigenvalue problem smooth LU decomposition Newton's method
DOI10.1137/140972494
Language英语
Funding ProjectNational Natural Science Foundation for Creative Research Groups[11021101] ; Hundred Talent Project of Chinese Academy of Sciences ; National Basic Research Program[2011CB309703] ; National Natural Science Foundation of China[11071118] ; National Natural Science Foundation of China[91118001]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000357407800018
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20314
Collection计算数学与科学工程计算研究所
Corresponding AuthorDai, Hua
Affiliation1.Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Dai, Hua,Bai, Zhong-Zhi,Wei, Ying. ON THE SOLVABILITY CONDITION AND NUMERICAL ALGORITHM FOR THE PARAMETERIZED GENERALIZED INVERSE EIGENVALUE PROBLEM[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2015,36(2):707-726.
APA Dai, Hua,Bai, Zhong-Zhi,&Wei, Ying.(2015).ON THE SOLVABILITY CONDITION AND NUMERICAL ALGORITHM FOR THE PARAMETERIZED GENERALIZED INVERSE EIGENVALUE PROBLEM.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,36(2),707-726.
MLA Dai, Hua,et al."ON THE SOLVABILITY CONDITION AND NUMERICAL ALGORITHM FOR THE PARAMETERIZED GENERALIZED INVERSE EIGENVALUE PROBLEM".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 36.2(2015):707-726.
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