Paper Info
Title
A refined harmonic Rayleigh-Ritz procedure and an explicitly restarted refined harmonic Arnoldi algorithm
Abstract
The work is fourfold. First, a refined harmonic Rayleigh-Ritz procedure is proposed, some relationships are established between the refined harmonic Ritz vector and the harmonic Ritz vector, an a priori error bound is derived for the refined harmonic Ritz vector, and some properties are established on Rayleigh quotients and residual norms. Second, a resulting refined harmonic Arnoldi method is discussed, and how to compute the refined harmonic Ritz vectors cheaply and accurately is considered. Third, an explicitly restarted refined harmonic Arnoldi algorithm is developed over an augmented Krylov subspace. Finally, numerical examples are reported that compare the new algorithm with the implicitly restarted harmonic Arnoldi algorithm (IRHA) and the implicitly restarted refined harmonic Arnoldi algorithm (IRRHA). Numerical results confirm efficiency of the new algorithm.
Year
DOI
Venue
2005
10.1016/j.mcm.2005.01.028
Mathematical and Computer Modelling
Keywords
Field
DocType
rayleigh quotients,new algorithm,harmonic rayleigh-ritz procedure,refined harmonic ritz vector,rayleigh quotient,harmonic ritz value,harmonic arnoldi algorithm,refined harmonic rayleigh-ritz procedure,harmonic ritz vector,numerical result,refined harmonic ritz,numerical example,harmonic arnoldi method,krylov subspace
Krylov subspace,Rayleigh–Ritz method,Residual,Mathematical optimization,Mathematical analysis,Arnoldi iteration,A priori and a posteriori,Quotient,Algorithm,Harmonic,Ritz method,Mathematics
Journal
Volume
Issue
ISSN
41
6-7
Mathematical and Computer Modelling
Citations 
PageRank 
References 
0
0.34
7
Authors
2
Name
Order
Citations
PageRank
Guizhi Chen131.42
Zhongxiao Jia212118.57