Geodesic
Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem
Applications of Mathematics, Tome 62 (2017) no. 4, pp. 357-375.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/AM.2017.0016-17
Classification : 15A18, 65F15
Keywords: SS-RR method; polynomial eigenvalue problem; balancing technique 
@article{10_21136_AM_2017_0016_17,
     author = {Chen, Hongjia and Imakura, Akira and Sakurai, Tetsuya},
     title = {Improving backward stability of {Sakurai-Sugiura} method with balancing technique in polynomial eigenvalue problem},
     journal = {Applications of Mathematics},
     pages = {357--375},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2017},
     doi = {10.21136/AM.2017.0016-17},
     mrnumber = {3686422},
     zbl = {06770049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0016-17/}
}
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
SP  - 357
EP  - 375
VL  - 62
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0016-17/
DO  - 10.21136/AM.2017.0016-17
LA  - en
ID  - 10_21136_AM_2017_0016_17
ER  - 
%0 Journal Article
%A Chen, Hongjia
%A Imakura, Akira
%A Sakurai, Tetsuya
%T Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem
%J Applications of Mathematics
%D 2017
%P 357-375
%V 62
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0016-17/
%R 10.21136/AM.2017.0016-17
%G en
%F 10_21136_AM_2017_0016_17
Chen, Hongjia; Imakura, Akira; Sakurai, Tetsuya. Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem. Applications of Mathematics, Tome 62 (2017) no. 4, pp. 357-375. doi : 10.21136/AM.2017.0016-17. http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0016-17/

Cité par Sources :