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Title: Recursive integral method with Cayley transformation
Summary

The recently developedRIM(recursive integral method) finds eigenvalues in a region of the complex plane. It computes an indicator to test if the region contains eigenvalues using an approximate spectral projection. If the indicator shows that the region contains eigenvalues, it is subdivided into smaller regions, which are then recursively tested and subdivided until any eigenvalues are isolated to a specified precision. We propose an enhancement toRIMthat uses Cayley transformations and Arnoldi's method to greatly decrease the number of factorizations required to solve the linear systems that arise from a discretized contour integral to compute the indicator, which substantially reduces the computational cost. We demonstrate the efficacy of our method with numerical examples and compare with the implicitly restarted Arnoldi method, as implemented ineigsin MATLAB.

 
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NSF-PAR ID:
10063887
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Numerical Linear Algebra with Applications
Volume:
25
Issue:
6
ISSN:
1070-5325
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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