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ON THE SOLVABILITY CONDITION AND NUMERICAL ALGORITHM FOR THE PARAMETERIZED GENERALIZED INVERSE EIGENVALUE PROBLEM

文献类型：期刊论文

作者Dai, Hua1; Bai, Zhong-Zhi2; Wei, Ying1
刊名SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
出版日期2015
卷号36期号:2页码:707-726
关键词inverse eigenvalue problem multiparameter eigenvalue problem smooth LU decomposition Newton's method
ISSN号0895-4798
DOI10.1137/140972494
英文摘要We 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.
资助项目National 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研究方向Mathematics
语种英语
WOS记录号WOS:000357407800018
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/20313]  
专题计算数学与科学工程计算研究所
通讯作者Dai, Hua
作者单位1.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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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