TY - JOUR
T1 - The palindromic generalized eigenvalue problem A*x = lambda Ax: Numerical solution and applications
AU - Li, Tiexiang
AU - Chiang, Chun-Yueh
AU - Chu, King-Wah
AU - Lin, Wen-wei
PY - 2011
Y1 - 2011
N2 - In this paper, we propose the palindromic doubling algorithm (PDA) for
the palindromic generalized eigenvalue problem (PGEP) A*x = lambda Ax.
We establish a complete convergence theory of the PDA for PGEPs
without unimodular eigenvalues, or with unimodular eigenvalues of
partial multiplicities two (one or two for eigenvalue 1). Some
important applications from the vibration analysis and the optimal
control for singular descriptor linear systems will be presented to
illustrate the feasibility and efficiency of the PDA.
AB - In this paper, we propose the palindromic doubling algorithm (PDA) for
the palindromic generalized eigenvalue problem (PGEP) A*x = lambda Ax.
We establish a complete convergence theory of the PDA for PGEPs
without unimodular eigenvalues, or with unimodular eigenvalues of
partial multiplicities two (one or two for eigenvalue 1). Some
important applications from the vibration analysis and the optimal
control for singular descriptor linear systems will be presented to
illustrate the feasibility and efficiency of the PDA.
UR - http://www.sciencedirect.com/science/article/pii/S0024379509006533
U2 - 10.1016/j.laa.2009.12.020
DO - 10.1016/j.laa.2009.12.020
M3 - Article
SN - 0024-3795
VL - 434
SP - 2269
EP - 2284
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 11
ER -