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A box‐shaped cyclically reduced operator
Author(s) -
Greif Chen,
Hocking Robert L.
Publication year - 2011
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.748
Subject(s) - mathematics , operator (biology) , biochemistry , chemistry , repressor , transcription factor , gene
Abstract We propose a new procedure of partial cyclic reduction, where we apply a 2 d ‐color ordering (with d =2, 3 the dimension of the problem), and use different operators for different gridpoints according to their color. These operators are chosen so that the gridpoints can be readily decoupled, and we then eliminate all colors but one. This yields a smaller cartesian mesh and box‐shaped 9‐point (in 2D) or 27‐point (in 3D) operators that are easy to analyze and implement. Multi‐line and multi‐plane orderings are considered, and we perform convergence analysis and numerical experiments that demonstrate the merits of our approach. Copyright © 2010 John Wiley & Sons, Ltd.