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Operator trigonometry of iterative methods
Author(s) -
Gustafson K.
Publication year - 1997
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/(sici)1099-1506(199707/08)4:4<333::aid-nla113>3.0.co;2-i
Subject(s) - lanczos resampling , generalized minimal residual method , mathematics , residual , trigonometry , iterative method , operator (biology) , algorithm , mathematical optimization , mathematical analysis , eigenvalues and eigenvectors , biochemistry , physics , chemistry , quantum mechanics , repressor , transcription factor , gene
A new and general approach to the understanding and analysis of widely used iterative methods for the numerical solution of the equation Ax = b is presented. This class of algorithms, which includes CGN, GMRES. ORTHOMIN, BCG, CGS, and others of current importance, utilizes residual norm minimizing procedures, such as those often found under the general names Galerkin method, Arnoldi method, Lanczos method, and so on. The view here is different: the needed error minimizations are seen trigonometrically. © 1997 John Wiley & Sons, Ltd.