Dissecting the FEAST algorithm for generalized eigenproblems

Details Dissecting the FEAST algorithm for generalized eigenproblems Dissecting the FEAST algorithm for generalized eigenproblems

2012-04-08

arxiv.org/abs/1204.1726v1

Computer Science

Numerical Analysis

11 Pages, 5 Figures. Submitted to Journal of Computational and Applied Mathematics

Scientific paper

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.

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