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Iterative solution of large linear systems with non‐smooth submatrices using partial wavelet transforms and split‐matrix matrix–vector multiplication
Author(s) -
González Patricia,
Cabaleiro José C.,
Pena Tomás F.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.881
Subject(s) - block matrix , matrix (chemical analysis) , mathematics , iterative method , matrix splitting , matrix multiplication , multiplication (music) , transformation matrix , algorithm , transformation (genetics) , row , wavelet , square matrix , symmetric matrix , combinatorics , computer science , eigenvalues and eigenvectors , physics , materials science , database , artificial intelligence , chemistry , composite material , quantum , biochemistry , kinematics , classical mechanics , quantum mechanics , gene
Abstract The iterative solution of large linear systems with highly irregular matrices cannot be accelerated by wavelet transformation and subsequent sparsification if the transformed matrix is still highly irregular. In this paper we show that if the irregularity of the original matrix is limited to a relatively small known set of rows or columns (as is the case in significant applications), then acceleration can be achieved by a mixed approach in which only the ‘smooth’ submatrix is transformed and iterative solution is implemented using a novel ‘split‐matrix’ form of matrix–vector multiplication. Copyright © 2003 John Wiley & Sons, Ltd.