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Recursive integral method with Cayley transformation
Author(s) -
Huang R.,
Sun J.,
Yang C.
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2199
Subject(s) - eigenvalues and eigenvectors , mathematics , transformation (genetics) , complex plane , matlab , discretization , projection (relational algebra) , methods of contour integration , algorithm , mathematical analysis , computer science , biochemistry , chemistry , gene , physics , quantum mechanics , operating system
Summary 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.