Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem

Chen, Hongjia, Imakura, Akira, and Sakurai, Tetsuya. "Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem." Applications of Mathematics 62.4 (2017): 357-375. <http://eudml.org/doc/294107>.

@article{Chen2017,
abstract = {One of the most efficient methods for solving the polynomial eigenvalue problem (PEP) is the Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR), which finds the eigenvalues contained in a certain domain using the contour integral. The SS-RR method converts the original PEP to a small projected PEP using the Rayleigh-Ritz projection. However, the SS-RR method suffers from backward instability when the norms of the coefficient matrices of the projected PEP vary widely. To improve the backward stability of the SS-RR method, we combine it with a balancing technique for solving a small projected PEP. We then analyze the backward stability of the SS-RR method. Several numerical examples demonstrate that the SS-RR method with the balancing technique reduces the backward error of eigenpairs of PEP.},
author = {Chen, Hongjia, Imakura, Akira, Sakurai, Tetsuya},
journal = {Applications of Mathematics},
keywords = {SS-RR method; polynomial eigenvalue problem; balancing technique},
language = {eng},
number = {4},
pages = {357-375},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem},
url = {http://eudml.org/doc/294107},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Chen, Hongjia
AU - Imakura, Akira
AU - Sakurai, Tetsuya
TI - Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 357
EP - 375
AB - One of the most efficient methods for solving the polynomial eigenvalue problem (PEP) is the Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR), which finds the eigenvalues contained in a certain domain using the contour integral. The SS-RR method converts the original PEP to a small projected PEP using the Rayleigh-Ritz projection. However, the SS-RR method suffers from backward instability when the norms of the coefficient matrices of the projected PEP vary widely. To improve the backward stability of the SS-RR method, we combine it with a balancing technique for solving a small projected PEP. We then analyze the backward stability of the SS-RR method. Several numerical examples demonstrate that the SS-RR method with the balancing technique reduces the backward error of eigenpairs of PEP.
LA - eng
KW - SS-RR method; polynomial eigenvalue problem; balancing technique
UR - http://eudml.org/doc/294107
ER -