Operator trigonometry of preconditioning, domain decomposition, sparse approximate inverses, successive overrelaxation, minimum residual schemes | Zendy

Gustafson Karl | Zendy

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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.

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