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Parallel iterative refinement in polynomial eigenvalue problems
Author(s) -
Campos Carmen,
Roman Jose E.
Publication year - 2016
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2052
Subject(s) - eigenvalues and eigenvectors , context (archaeology) , iterative method , scalability , polynomial , iterative refinement , mathematics , computation , mathematical optimization , computer science , matrix (chemical analysis) , linear algebra , coefficient matrix , matrix polynomial , iterative and incremental development , newton's method , algorithm , nonlinear system , mathematical analysis , paleontology , physics , materials science , geometry , software engineering , quantum mechanics , database , composite material , biology
Summary Methods for the polynomial eigenvalue problem sometimes need to be followed by an iterative refinement process to improve the accuracy of the computed solutions. This can be accomplished by means of a Newton iteration tailored to matrix polynomials. The computational cost of this step is usually higher than the cost of computing the initial approximations, due to the need of solving multiple linear systems of equations with a bordered coefficient matrix. An effective parallelization is thus important, and we propose different approaches for the message‐passing scenario. Some schemes use a subcommunicator strategy in order to improve the scalability whenever direct linear solvers are used. We show performance results for the various alternatives implemented in the context of SLEPc, the Scalable Library for Eigenvalue Problem Computations. Copyright © 2016 John Wiley & Sons, Ltd.