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A dual adaptive procedure for the automatic determination of iteration parameters for Chebyshev acceleration
Author(s) -
Mai TsunZee,
Young David M.
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620270305
Subject(s) - chebyshev filter , acceleration , eigenvalues and eigenvectors , chebyshev iteration , mathematics , iterative method , mathematical optimization , matrix (chemical analysis) , chebyshev polynomials , algorithm , mathematical analysis , physics , materials science , classical mechanics , quantum mechanics , composite material
Chebyshev acceleration for a symmetrizable basic iterative method u ( n +1) = Gu ( n ) + k ; requires estimates of the extreme eigenvalues m ( G ) and M ( G ) of the iteration matrix G . Adaptive procedures are often used in order to obtain good estimates for m ( G ) and M ( G ). Some existing adaptive procedures are able to give an estimate of either m ( G ) or M ( G ) but not both on any given iteration. In this paper we present an adaptive procedure which can estimate both m ( G ) and M ( G ) at the same time and which has other useful properties. Numerical results are given which show the new procedure usually requires fewer iterations than previous procedures.