Premium
Application of the three‐way decomposition for matrix compression
Author(s) -
Ibraghimov Ilghiz
Publication year - 2002
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.297
Subject(s) - preconditioner , mathematics , matrix (chemical analysis) , arithmetic function , compression (physics) , matrix decomposition , grid , computational complexity theory , arithmetic , algebra over a field , algorithm , linear system , discrete mathematics , pure mathematics , eigenvalues and eigenvectors , mathematical analysis , geometry , materials science , physics , quantum mechanics , composite material
We present a new method to compress and invert 3D integral operators on rectangular non‐regular grids. This method requires a small amount of memory to store the compressed matrix and in most cases can provide a good preconditioner for the solution of linear systems with this matrix. We demonstrate efficiency of this method for the solution of some model discrete problems associated with ∫ ℝ 3A ( x̄ , ȳ ) f ( x̄ )d x̄ = u ( ȳ ), x̄ , ȳ ϵℝ 3 , where A ( x̄ , ȳ ) such as 1/∣ x̄ − ȳ ∣ is considered on a non‐regular grid. The arithmetical complexity of matrix–vector and preconditioner–vector multiplications are about N 4/3 operations and there are only about N 2/3 words of memory to store. Copyright © 2002 John Wiley & Sons, Ltd.