Premium
Using the modified 2nd order incomplete Cholesky decomposition as the conjugate gradient preconditioning
Author(s) -
Kaporin I. E.
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.296
Subject(s) - cholesky decomposition , incomplete cholesky factorization , preconditioner , conjugate gradient method , mathematics , minimum degree algorithm , finite element method , linear system , order (exchange) , incomplete lu factorization , factorization , mathematical optimization , matrix decomposition , algorithm , eigenvalues and eigenvectors , mathematical analysis , physics , finance , quantum mechanics , economics , thermodynamics
In this paper, the ‘second‐order’ incomplete triangular factorization (Kaporin, 1998) is considered as a preconditioner for the CG method. Some refinements of the original algorithm are proposed and investigated, which give rise to a more efficient modified incomplete Cholesky 2nd‐order (MIC2) type preconditionings. Numerical results are given for a set of real‐life large‐scale SPD linear systems arising in the finite element modelling of linear elasticity problems which clearly indicate the superiority of the MIC2 preconditionings. Copyright © 2002 John Wiley & Sons, Ltd.