Spectral Indicator Method with Cayley Transformation for Eigenvalue Problems

Date
10/2/2017
Location
4:30PM at UNIV 103
Speaker
Jiguang Sun, Michigan Technological University
Title
Spectral Indicator Method with Cayley Transformation for Eigenvalue Problems
Host
Description

Recently, a non-classical eigenvalue solver, called RIM, was proposed to compute (all) eigenvalues in a region on the complex plane. Without solving any eigenvalue problem, it tests if a region contains eigenvalues using an approximate spectral projection. Regions that contain eigenvalues are subdivided and tested recursively until eigenvalues are isolated with a specified precision. This makes RIM an eigensolver distinct from all existing methods. Furthermore, it requires no a priori spectral information. In this paper, we propose an improved version of RIM for non-Hermitian eigenvalue problems. Using Cayley transformation and Krylov subspace methods, the computation cost is reduced significantly. Effectiveness and efficiency of the new method are demonstrated by numerical examples and compared with 'eigs' in Matlab.