Dissecting the FEAST algorithm for generalized eigenproblems

Authors:
Lukas KräMer;Edoardo Di Napoli;Martin Galgon;Bruno Lang;Paolo Bientinesi
Affiliations:
Bergische Universität Wuppertal, Fachbereich C-Mathematik und Naturwissenschaften, Gauístr. 20, 42119 Wuppertal, Germany;Forschungszentrum Jülich, Institute for Advanced Simulation, Jülich Supercomputing Centre, 52425 Jülich, Germany;Bergische Universität Wuppertal, Fachbereich C-Mathematik und Naturwissenschaften, Gauístr. 20, 42119 Wuppertal, Germany;Bergische Universität Wuppertal, Fachbereich C-Mathematik und Naturwissenschaften, Gauístr. 20, 42119 Wuppertal, Germany;RWTH Aachen, AICES, Schinkelstr. 2, 52062 Aachen, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

We analyze the FEAST method for computing selected eigenvalues and eigenvectors of large sparse matrix pencils. After establishing the close connection between FEAST and the well-known Rayleigh-Ritz method, we identify several critical issues that influence convergence and accuracy of the solver: the choice of the starting vector space, the stopping criterion, how the inner linear systems impact the quality of the solution, and the use of FEAST for computing eigenpairs from multiple intervals. We complement the study with numerical examples, and hint at possible improvements to overcome the existing problems.