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The restarted shift‐and‐invert Krylov method for matrix functions
Author(s) -
Moret Igor,
Popolizio Marina
Publication year - 2014
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.1862
Subject(s) - mathematics , matrix (chemical analysis) , selection (genetic algorithm) , simple (philosophy) , matrix function , class (philosophy) , fraction (chemistry) , krylov subspace , algorithm , algebra over a field , iterative method , computer science , pure mathematics , symmetric matrix , philosophy , eigenvalues and eigenvectors , materials science , physics , chemistry , organic chemistry , epistemology , quantum mechanics , artificial intelligence , composite material
SUMMARY In this paper, the numerical evaluation of matrix functions expressed in partial fraction form is addressed. The shift‐and‐invert Krylov method is analyzed, with special attention to error estimates. Such estimates give insights into the selection of the shift parameter and lead to a simple and effective restart procedure. Applications to the class of Mittag–Leffler functions are presented. Copyright © 2012 John Wiley & Sons, Ltd.