DocumentCode
404634
Title
A novel approach to the shifted QR algorithm for the Hermitian eigenvalue problem
Author
Nikpour, M. ; Manton, J.H. ; Mareels, I.M.Y.
Author_Institution
Dept. of Electr. & Electron. Eng., Melbourne Univ., Vic., Australia
Volume
3
fYear
2003
fDate
9-12 Dec. 2003
Firstpage
2364
Abstract
We present two novel algorithms for computing the eigenvectors of an Hermitian matrix. The algorithms are based on the shifted QR algorithm. We show how viewing the shifted QR algorithm in terms of subspace iteration and Rayleigh quotient iteration (RQI) can lead to algorithms which are more naturally suited to adaptive computation of the eigenstructure of Hermitian matrices than the standard algorithm. We also show the algorithms to be theoretically similar to each other.
Keywords
Hermitian matrices; eigenvalues and eigenfunctions; iterative methods; Hermitian eigenvalue problem; Hermitian matrix; Rayleigh quotient iteration; eigenvectors; shifted QR algorithm; subspace iteration; Artificial intelligence; Australia Council; Computational complexity; Convergence; Eigenvalues and eigenfunctions; Gold; Linear algebra; Newton method; Optimization methods; Spine;
fLanguage
English
Publisher
ieee
Conference_Titel
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on
ISSN
0191-2216
Print_ISBN
0-7803-7924-1
Type
conf
DOI
10.1109/CDC.2003.1272972
Filename
1272972
Link To Document