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Generalized Rybicki Press algorithm
Author(s) -
Ambikasaran Sivaram
Publication year - 2015
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.2003
Subject(s) - mathematics , algorithm , matrix (chemical analysis) , separable space , covariance matrix , exponential function , scaling , gaussian elimination , algebra over a field , gaussian , pure mathematics , geometry , mathematical analysis , materials science , physics , quantum mechanics , composite material
Summary This article discusses a more general and numerically stable Rybicki Press algorithm, which enables inverting and computing determinants of covariance matrices, whose elements are sums of exponentials. The algorithm is true in exact arithmetic and relies on introducing new variables and corresponding equations, thereby converting the matrix into a banded matrix of larger size. Linear complexity banded algorithms for solving linear systems and computing determinants on the larger matrix enable linear complexity algorithms for the initial semi‐separable matrix as well. Benchmarks provided illustrate the linear scaling of the algorithm. Copyright © 2015 John Wiley & Sons, Ltd.