IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
On Correction-Based Iterative Methods for Eigenvalue Problems
Takafumi MIYATA
Author information
JOURNAL RESTRICTED ACCESS

2018 Volume E101.A Issue 10 Pages 1668-1675

Details
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.

Content from these authors
© 2018 The Institute of Electronics, Information and Communication Engineers
Previous article Next article
feedback
Top