HSL MI28: An Efficient and Robust Limited-Memory Incomplete Cholesky Factorization Code

0422618 - ÚI 2015 RIV US eng J - Článek v odborném periodiku
Scott, J. - Tůma, Miroslav
HSL MI28: An Efficient and Robust Limited-Memory Incomplete Cholesky Factorization Code.
ACM Transactions on Mathematical Software. Roč. 40, č. 4 (2014), Article number 24. ISSN 0098-3500. E-ISSN 1557-7295
Grant CEP: GA ČR GA13-06684S
Grant ostatní: EPSRC(GB) EP/I013067/1
Institucionální podpora: RVO:67985807
Klíčová slova: preconditioning * sparse linear systems * incomplete decompositions * preconditioned iterative methods
Kód oboru RIV: IN - Informatika
Impakt faktor: 1.863, rok: 2014

This paper focuses on the design and development of a new robust and efficient general-purpose incomplete Cholesky factorization package HSL MI28, which is available within the HSL mathematical software library. It implements a limited memory approach that exploits ideas from the positive semidefinite Tismenetsky-Kaporin modification scheme and, through the incorporation of intermediate memory, is a generalization of the widely-used ICFS algorithm of Lin and Moré. Both the density of the incomplete factor and the amount of memory used in its computation are under the user’s control. The performance of HSL MI28 is demonstrated using extensive numerical experiments involving a large set of test problems arising from a wide range of real-world applications. The numerical experiments are used to isolate the effects of scaling, ordering and dropping strategies so as to assess their usefulness in the development of robust algebraic incomplete factorization preconditioners and to select default settings for HSL MI28. They also illustrate the significant advantage of employing a modest amount of intermediate memory. Furthermore, the results demonstrate that, with limited memory, high quality yet sparse general-purpose preconditioners are obtained. Comparisons are made with ICFS, with a level-based incomplete factorization code and, finally, with a state-of-the-art direct solver.
Trvalý link: http://hdl.handle.net/11104/0228782