Zolotarev quadrature rules and load balancing for the FEAST eigensolver

Güttel, Stefan and Polizzi, Eric and Tang, Peter and Viaud, Gautier (2014) Zolotarev quadrature rules and load balancing for the FEAST eigensolver. [MIMS Preprint]

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Abstract

The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function. We propose improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximants based on the work of Zolotarev. Numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues. The new approach improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.

Item Type: MIMS Preprint
Uncontrolled Keywords: generalized eigenproblem, FEAST, quadrature, Zolotarev, filter design, load balancing
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 41 Approximations and expansions
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 30 Jul 2014
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2163

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