A new algorithm for the generalized eigenvalue problem

被引：0

作者：

Huper, K

Helmke, U

机构：

来源：

1997 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS I - V: VOL I: PLENARY, EXPERT SUMMARIES, SPECIAL, AUDIO, UNDERWATER ACOUSTICS, VLSI; VOL II: SPEECH PROCESSING; VOL III: SPEECH PROCESSING, DIGITAL SIGNAL PROCESSING; VOL IV: MULTIDIMENSIONAL SIGNAL PROCESSING, NEURAL NETWORKS - VOL V: STATISTICAL SIGNAL AND ARRAY PROCESSING, APPLICATIONS | 1997年

关键词：

D O I：

暂无

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

The problem of finding the generalized eigenvalues and eigenvectors of a pair of real symmetric matrices A and B, with B > 0, can be viewed as a smooth optimization problem on a smooth manifold. We present a cost function approach to the generalized eigenvalue problem which is posed on the product of the n-sphere and Euclidian space R. The critical point set of this cost function is studied. An algorithm is presented based on constrained optimization. A proof of local quadratic convergence is given.

引用

页码：35 / 38

页数：4

共 50 条

[31] New perturbation bounds of partitioned generalized Hermitian eigenvalue problem
Xiao, Chuanfu
Li, Hanyu
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2018, 321 : 422 - 430
[32] On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem
Yuji Nakatsukasa
[J]. Numerische Mathematik, 2012, 121 : 531 - 544
[33] Numerical enclosure for each eigenvalue in generalized eigenvalue problem
Miyajima, Shinya
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (09) : 2545 - 2552
[34] On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem
Nakatsukasa, Yuji
[J]. NUMERISCHE MATHEMATIK, 2012, 121 (03) : 531 - 544
[35] A linear eigenvalue algorithm for the nonlinear eigenvalue problem
Elias Jarlebring
Wim Michiels
Karl Meerbergen
[J]. Numerische Mathematik, 2012, 122 : 169 - 195
[36] A linear eigenvalue algorithm for the nonlinear eigenvalue problem
Jarlebring, Elias
Michiels, Wim
Meerbergen, Karl
[J]. NUMERISCHE MATHEMATIK, 2012, 122 (01) : 169 - 195
[37] A MULTIGRID METHOD FOR THE GENERALIZED SYMMETRICAL EIGENVALUE PROBLEM .1. ALGORITHM AND IMPLEMENTATION
HWANG, T
PARSONS, ID
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1992, 35 (08) : 1663 - 1676
[38] AN ALGORITHM FOR THE GENERALIZED EIGENVALUE PROBLEM FOR NONSQUARE MATRIX PENCILS BY MINIMAL PERTURBATION APPROACH
Ito, Shinji
Murota, Kazuo
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2016, 37 (01) : 409 - 419
[39] New algorithm for solving the inverse eigenvalue problem of a Jacobi matrix
[J]. Nanjing Hangkong Hangtian Daxue Xuebao, 6 (766-771):
[40] ONE GENERALIZED QUASILINEAR EIGENVALUE PROBLEM
MAKHMUDOV, AP
[J]. DOKLADY AKADEMII NAUK SSSR, 1978, 243 (01): : 33 - 36

← 1 2 3 4 5 →