SOLVING LARGE-SCALE QUADRATIC EIGENVALUE PROBLEMS WITH HAMILTONIAN EIGENSTRUCTURE USING A STRUCTURE-PRESERVING KRYLOV SUBSPACE METHOD

被引：0

作者：

Benner, Peter ^{[1
]}

Fassbender, Heike ^{[2
]}

Stoll, Martin ^{[3
]}

机构：

[1] TU Chemnitz, Fak Math Math Ind & Tech, D-09107 Chemnitz, Germany

[2] TU Braunschweig, Inst Computat Math, AG Numer, D-38023 Braunschweig, Germany

[3] Math Inst, Oxford OX1 3LB, England

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2007年 / 29卷

关键词：

quadratic eigenvalue problem; Hamiltonian symmetry; Krylov subspace method; symplectic Lanczos process; gyroscopic systems;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the numerical solution of quadratic eigenproblems with spectra that exhibit Hamiltonian symmetry. We propose to solve such problems by applying a Krylov-Schur-type method based on the symplectic Lanczos process to a structured linearization of the quadratic matrix polynomial. In order to compute interior eigenvalues, we discuss several shift-and-invert operators with Hamiltonian structure. Our approach is tested for several examples from structural analysis and gyroscopic systems.

引用

页码：212 / 229

页数：18

共 50 条

[31] Memory-efficient Krylov subspace techniques for solving large-scale Lyapunov equations
Kressner, Daniel
2008 IEEE INTERNATIONAL SYMPOSIUM ON COMPUTER-AIDED CONTROL SYSTEM DESIGN, 2008, : 207 - 212
[32] Solving large-scale eigenvalue problems on vector parallel processors
Harrar, DL
Osborne, MR
VECTOR AND PARALLEL PROCESSING - VECPAR'98, 1999, 1573 : 100 - 113
[33] STRUCTURE-PRESERVING ALGORITHMS FOR PALINDROMIC QUADRATIC EIGENVALUE PROBLEMS ARISING FROM VIBRATION OF FAST TRAINS
Huang, Tsung-Ming
Lin, Wen-Wei
Qian, Jiang
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (04) : 1566 - 1592
[34] New model correcting method for quadratic eigenvalue problems using symmetric eigenstructure assignment
Kuo, YC
Lin, WW
Xu, SF
AIAA JOURNAL, 2005, 43 (12) : 2593 - 2598
[35] New model correcting method for quadratic eigenvalue problems using symmetric eigenstructure assignment
Kuo, Y.-C. (m883207@am.nthu.edu.tw), 1600, American Inst. Aeronautics and Astronautics Inc. (43):
[36] General minimal residual Krylov subspace method for large-scale model reduction
Jaimoukha, IM
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1997, 42 (10) : 1422 - 1427
[37] A decomposition algorithm for solving large-scale quadratic programming problems
Li, HM
Zhang, KC
APPLIED MATHEMATICS AND COMPUTATION, 2006, 173 (01) : 394 - 403
[38] Deep Neighborhood Structure-Preserving Hashing for Large-Scale Image Retrieval
Qin, Qibing
Xie, Kezhen
Zhang, Wenfeng
Wang, Chengduan
Huang, Lei
IEEE TRANSACTIONS ON MULTIMEDIA, 2024, 26 : 1881 - 1893
[39] O(N) Krylov-subspace method for large-scale ab initio electronic structure calculations
Ozaki, Taisuke
PHYSICAL REVIEW B, 2006, 74 (24)
[40] On some Krylov subspace based methods for large-scale nonsymmetric algebraic Riccati problems
Bentbib, A.
Jbilou, K.
Sadek, E. M.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (10) : 2555 - 2565

← 1 2 3 4 5 →