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Algorithms for construction of preconditioners based on incomplete block‐factorizations of the matrix
Author(s) -
Vassilevski P. S.
Publication year - 1989
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.1620270312
Subject(s) - incomplete lu factorization , conjugate gradient method , incomplete cholesky factorization , tridiagonal matrix , mathematics , factorization , block (permutation group theory) , discretization , sparse matrix , matrix (chemical analysis) , algorithm , matrix decomposition , algebra over a field , combinatorics , pure mathematics , mathematical analysis , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material , gaussian
When applying an incomplete block‐factorization technique one needs sparse approximate inverses of the successive Schur complements computed throughout the factorization. Here we propose a method for the construction of such sparse approximate inverses. The method has an advantage over earlier versions, in that such approximate inverses of block‐tridiagonal matrices can be computed in parallel. Comparative numerical experiments for solving a number of discretized diffusion equations by this preconditioning matrix in a preconditioned conjugate gradient method and earlier versions of incomplete block‐factorization preconditioners are presented.