Premium
Operator trigonometry of preconditioning, domain decomposition, sparse approximate inverses, successive overrelaxation, minimum residual schemes
Author(s) -
Gustafson Karl
Publication year - 2003
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.289
Subject(s) - trigonometry , mathematics , residual , operator (biology) , lemma (botany) , convergence (economics) , domain decomposition methods , algorithm , mathematical analysis , finite element method , ecology , biochemistry , chemistry , poaceae , repressor , biology , transcription factor , economics , gene , economic growth , physics , thermodynamics
This paper extends the relationship between the author's operator trigonometry and convergence rates and other properties of important iterative methods. A new interesting trigonometric preconditioning lemma is given. The general relationship between domain decomposition methods and the operator trigonometry is established. A new basic conceptual link between sparse approximate inverse algorithms and the operator trigonometry is observed. A new underlying fundamental inherent trigonometry of the classical successive over‐relaxation scheme is exposed. Some improved trigonometric interpretations of minimum residual schemes are mentioned. Copyright © 2002 John Wiley & Sons, Ltd.