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On the Non‐Hierarchical Preconditioner Constructions
Author(s) -
Kiss B.
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410302
Subject(s) - preconditioner , schur complement , multiplication (music) , mathematics , matrix representation , matrix (chemical analysis) , matrix multiplication , algebra over a field , complement (music) , norm (philosophy) , representation (politics) , arithmetic , pure mathematics , combinatorics , algorithm , eigenvalues and eigenvectors , iterative method , physics , chemistry , law , quantum , biochemistry , quantum mechanics , political science , complementation , politics , group (periodic table) , gene , phenotype , chromatography
In this paper a new cyclic matrix representation of the H –1/2 norm is presented. Its application as Schur complement preconditioning matrix requires only matrix‐vector multiplication. The computational cost of this matrix‐vector multiplication is O ( N · log( N )) arithmetic operations, where N is the number of unknowns. The efficiency of the construction to elliptic problems has been verified by numerical tests. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)