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Two‐grid methods for banded linear systems from DCT III algebra
Author(s) -
Chan R. H.,
SerraCapizzano S.,
TablinoPossio C.
Publication year - 2004
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.399
Subject(s) - mathematics , multigrid method , linear algebra , coefficient matrix , polynomial , rate of convergence , grid , convergence (economics) , constant (computer programming) , matrix (chemical analysis) , discrete cosine transform , linear system , numerical linear algebra , algebra over a field , differential equation , mathematical analysis , pure mathematics , geometry , computer science , image (mathematics) , artificial intelligence , quantum mechanics , eigenvalues and eigenvectors , physics , economics , channel (broadcasting) , computer network , materials science , economic growth , composite material , programming language
We describe a two‐grid and a multigrid method for linear systems whose coefficient matrices are point or block matrices from the cosine algebra generated by a polynomial. We show that the convergence rate of the two‐grid method is constant independent of the size of the given matrix. Numerical examples from differential and integral equations are given to illustrate the convergence of both the two‐grid and the multigrid method. Copyright © 2004 John Wiley & Sons, Ltd.