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Krylov subspace accelerated inexact Newton method for linear and nonlinear equations
Author(s) -
Harrison Robert J.
Publication year - 2004
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.10108
Subject(s) - krylov subspace , subspace topology , nonlinear system , inversion (geology) , computer science , simple (philosophy) , iterative method , mathematics , newton's method , energy (signal processing) , algorithm , physics , quantum mechanics , artificial intelligence , paleontology , philosophy , epistemology , structural basin , biology
A Krylov subspace accelerated inexact Newton (KAIN) method for solving linear and nonlinear equations is described, and its relationship to the popular direct inversion in the iterative subspace method [DIIS; Pulay, P., Chem Phys Lett 1980, 393, 73] is analyzed. The two methods are compared with application to simple test equations and the location of the minimum energy crossing point of potential energy surfaces. KAIN is no more complicated to implement than DIIS, but can accommodate a wider variety of preconditioning and performs substantially better with poor preconditioning. With perfect preconditioning, KAIN is shown to be very similar to DIIS. For these reasons, KAIN is recommended as a replacement for DIIS. © 2003 Wiley Periodicals, Inc. J Comput Chem 25: 328–334, 2004