On Positive Semidefinite Modification Schemes for Incomplete Cholesky Factorization

0428296 - ÚI 2015 RIV US eng J - Journal Article
Scott, J. - Tůma, Miroslav
On Positive Semidefinite Modification Schemes for Incomplete Cholesky Factorization.
SIAM Journal on Scientific Computing. Roč. 36, č. 2 (2014), A609-A633. ISSN 1064-8275. E-ISSN 1095-7197
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : sparse matrices * sparse linear systems * positive-definite symmetric systems * iterative solvers * preconditioning * incomplete Cholesky factorization
Subject RIV: BA - General Mathematics
Impact factor: 1.854, year: 2014

Incomplete Cholesky factorizations have long been important as preconditioners for use in solving large-scale symmetric positive-definite linear systems. In this paper, we focus on the relationship between two important positive semidefinite modification schemes that were introduced to avoid factorization breakdown, namely, the approach of Jennings and Malik and that of Tismenetsky. We present a novel view of the relationship between the two schemes and implement them in combination with a limited memory approach. We explore their effectiveness using extensive numerical experiments involving a large set of test problems arising from a wide range of practical applications.
Permanent Link: http://hdl.handle.net/11104/0233652