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

doi:10.1137/140972494

	ON THE SOLVABILITY CONDITION AND NUMERICAL ALGORITHM FOR THE PARAMETERIZED GENERALIZED INVERSE EIGENVALUE PROBLEM
	Dai, Hua 1; Bai, Zhong-Zhi2 ; Wei, Ying 1
	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.