The open archive for STFC research publications

Full Record Details

Persistent URL http://purl.org/net/epubs/work/66079
Record Status Checked
Record Id 66079
Title On positive semidefinite modification schemes for incomplete Cholesky factorization
Abstract For large-scale sparse symmetric positive-definite linear systems of equations Ax = b an important class of preconditioners is represented by incomplete Cholesky factorizations, that is, factorizations of the form LL(T) in which some of the fill entries that would occur in a complete factorization are ignored. Over the last 60 years or so, many different types of incomplete factorization methods have been developed, some inspired by particular applications and some intended to be more general-purpose. In this talk, we consider two important modification schemes that were introduced to avoid factorization breakdown (that is, zero or negative pivots): that of Jennings and Malik (1977) and that of Tismenetsky (1991). We explore the relationship between the two approaches and, based on our new understanding of them, we present an enhanced incomplete Cholesky factorization algorithm. Our approach uses limited memory (both limited memory for L and limited intermediate memory during its computation), incorporates diagonal shifting in the event of breakdown, and allows the use of drop tolerances. The proposed algorithm is implemented in a new library-quality software package HSL_MI28. The performance of HSL_MI28 is demonstrated using extensive numerical experiments involving a wide range of problems arising from practical pplications.
Organisation STFC , SCI-COMP , SCI-COMP-CM
Keywords Incomplete Cholesky factorization , Sparse symmetric linear system
Funding Information
Related Research Object(s):
Licence Information:
Language English (EN)
Type Details URI(s) Local file(s) Year
Presentation Presented at International Conference On Preconditioning Techniques For Scientific And Industrial Applications, Oxford, UK, 19-21 Jun 2013. precond13.pdf 2013