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 -