Using the modified 2nd order incomplete Cholesky decomposition as the conjugate gradient preconditioning | Zendy

Kaporin I. E. | Zendy

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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.

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