KMS Of Academy of mathematics and systems sciences, CAS
ON THE SOLVABILITY CONDITION AND NUMERICAL ALGORITHM FOR THE PARAMETERIZED GENERALIZED INVERSE EIGENVALUE PROBLEM | |
Dai, Hua1; Bai, Zhong-Zhi2; Wei, Ying1 | |
2015 | |
发表期刊 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
ISSN | 0895-4798 |
卷号 | 36期号:2页码:707-726 |
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. |
关键词 | inverse eigenvalue problem multiparameter eigenvalue problem smooth LU decomposition Newton's method |
DOI | 10.1137/140972494 |
语种 | 英语 |
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 |
WOS类目 | Mathematics, Applied |
WOS记录号 | WOS:000357407800018 |
出版者 | SIAM PUBLICATIONS |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/20314 |
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. |
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