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Exact interpolation scheme with approximation vector used as a column of the prolongator
Author(s) -
Kužel Roman,
Vaněk Petr
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.1975
Subject(s) - interpolation (computer graphics) , mathematics , linear interpolation , column (typography) , scheme (mathematics) , space (punctuation) , acceleration , range (aeronautics) , basis (linear algebra) , exact solutions in general relativity , mathematical optimization , algorithm , mathematical analysis , geometry , computer science , connection (principal bundle) , physics , animation , computer graphics (images) , materials science , classical mechanics , polynomial , composite material , operating system
Summary Our method is a kind of exact interpolation scheme by Achi Brandt et al . In the exact interpolation scheme, for x being the fine‐level approximation of the solution, the coarse‐space V = V ( x ) is constructed so that x satisfies x ∈ V . We achieve it simply by adding the vector x as a first column of the prolongator. (The columns of the prolongator P form a computationally relevant basis of the coarse‐space V = Range( P ).) The advantages of this construction become obvious when solving non‐linear problems. The cost of enriching the coarse‐space V by the current approximation x is a single dense column of the prolongator that has to be updated each iteration. Our method can be used for multilevel acceleration of virtually any iterative method used for solving both linear and non‐linear systems. Copyright © 2015 John Wiley & Sons, Ltd.