Rational and polynomial filtering for eigenvalue problems

Yuanzhe Xi
Department of Computer Science and Engineering University of Minnesota

Room:  DCH 1049

Sep 29, 2016 2:00 PM CST

Two  filtering techniques are presented  for solving large Hermitian eigenvalue problems by the method of spectrum slicing that consists of subdividing the spectrum in a number of subintervals and computing eigenvalues in each subinterval independently. In the first approach, the  filter is a  polynomial constructed as the least-squares approximation to an appropriately centered Dirac distribution. The second approach targets matrices whose spectral distribution is very irregular, as well as generalized eigenvalue problems. It is based on using a rational filter in a least-squares sense. The efficiency and robustness of the proposed methods are demonstrated through some Hamiltonian matrices from electronic structure calculations.

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