Recursive Integral Eigenvalue Solver with Cayley Transformation

Thursday, February 23, 2017 - 11:00am - 12:00pm
Lind 305
Jiguang Sun (Michigan Technological University)
Recently, a non-classical eigenvalue solver, called {\bf RIM}, was proposed to compute (all) eigenvalues in a region on the complex plane. Without solving any eigenvalue problems, 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 {\bf RIM} an eigenvalue solver distinct from all existing methods. Furthermore, it requires no a priori spectral information. In this talk, we implement an improved version of {\bf RIM} for non-Hermitian eigenvalue problems. Using Cayley transforms, the computation cost is reduced significantly also it inherits all the advantages of RIM. Numerical examples are presented and compared with 'eigs' in Matlab.