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Parallel Newton two‐stage methods based on ILU factorizations for nonlinear systems
Author(s) -
Arnal J.,
Migallón H.,
Migallón V.,
Penadés J.
Publication year - 2006
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.488
Subject(s) - newton's method , chord (peer to peer) , nonlinear system , iterative method , mathematics , convergence (economics) , computer science , algorithm , mathematical optimization , distributed computing , physics , quantum mechanics , economics , economic growth
Parallel iterative algorithms based on the Newton method and on two of its variants, the Shamanskii method and the Chord method, for solving nonlinear systems are proposed. These algorithms are based on two‐stage multisplitting methods where incomplete LU factorizations are considered as a mean of constructing the inner splittings. Convergence properties of these parallel methods are studied for H ‐matrices. Computational results of these methods on two parallel computing systems are discussed. The reported experiments show the effectiveness of these methods. Copyright © 2006 John Wiley & Sons, Ltd.