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Reliable preconditioned iterative linear solvers for some numerical integrators
Author(s) -
Bertaccini D.
Publication year - 2001
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 - 10.1002/1099-1506(200103)8:2<111::aid-nla234>3.0.co;2-q
Subject(s) - preconditioner , mathematics , circulant matrix , integrator , linear system , ordinary differential equation , exponential integrator , block (permutation group theory) , numerical analysis , boundary value problem , iterative method , multigrid method , partial differential equation , differential equation , algorithm , differential algebraic equation , mathematical analysis , computer science , geometry , computer network , bandwidth (computing)
Implicit time‐step numerical integrators for ordinary and evolutionary partial differential equations need, at each step, the solution of linear algebraic equations that are unsymmetric and often large and sparse. Recently, a block preconditioner based on circulant approximations for the linear systems arising in the boundary value methods (BVMs) was introduced by the author. Here, some circulant approximations are compared and a further new type is considered. Numerical experiments are presented to check the effectiveness of the various approximations that can be used in the underlying block preconditioner. Copyright © 2001 John Wiley & Sons, Ltd.