Paper Info
Title
On Correction-Based Iterative Methods For Eigenvalue Problems
Abstract
The Jacobi-Davidson method and the Riccati method for eigenvalue problems are studied. In the methods, one has to solve a nonlinear equation called the correction equation per iteration, and the difference between the methods comes from how to solve the equation. In the Jacobi-Davidson/Riccati method the correction equation is solved with/without linearization. In the literature, avoiding the linearization is known as an improvement to get a better solution of the equation and bring the faster convergence. In fact, the Riccati method showed superior convergence behavior for some problems. Nevertheless the advantage of the Riccati method is still unclear, because the correction equation is solved not exactly but with low accuracy. In this paper, we analyzed the approximate solution of the correction equation and clarified the point that the Riccati method is specialized for computing particular solutions of eigenvalue problems. The result suggests that the two methods should be selectively used depending on target solutions. Our analysis was verified by numerical experiments.
Year
DOI
Venue
2018
10.1587/transfun.E101.A.1668
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
Keywords
Field
DocType
numerical analysis, eigenvalue and eigenvector, iterative method, correction equation
Applied mathematics,Iterative method,Theoretical computer science,Mathematics,Eigenvalues and eigenvectors
Journal
Volume
Issue
ISSN
E101A
10
0916-8508
Citations 
PageRank 
References 
1
0.37
0
Authors
1
Name
Order
Citations
PageRank
Takafumi Miyata111.39