Recursive integral method with Cayley transformation
Document Type
Article
Publication Date
7-10-2018
Department
Department of Mathematical Sciences
Abstract
The recently developed RIM (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 to RIM that 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 in eigs in MATLAB.
Publication Title
Numerical Linear Algebra with Applications
Recommended Citation
Huang, R.,
Sun, J.,
&
Yang, C.
(2018).
Recursive integral method with Cayley transformation.
Numerical Linear Algebra with Applications,
25(6).
http://doi.org/10.1002/nla.2199
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/259
Publisher's Statement
© 2018 John Wiley & Sons, Ltd. Publisher's version of record: https://doi.org/10.1002/nla.2199