Block sparse Cholesky algorithms on advanced uniprocessor computers

Technical Report · Sun Dec 01 04:00:00 EST 1991

DOI:https://doi.org/10.2172/6097949· OSTI ID:6097949

Ng, E G; Peyton, B W

As with many other linear algebra algorithms, devising a portable implementation of sparse Cholesky factorization that performs well on the broad range of computer architectures currently available is a formidable challenge. Even after limiting our attention to machines with only one processor, as we have done in this report, there are still several interesting issues to consider. For dense matrices, it is well known that block factorization algorithms are the best means of achieving this goal. We take this approach for sparse factorization as well. This paper has two primary goals. First, we examine two sparse Cholesky factorization algorithms, the multifrontal method and a blocked left-looking sparse Cholesky method, in a systematic and consistent fashion, both to illustrate the strengths of the blocking techniques in general and to obtain a fair evaluation of the two approaches. Second, we assess the impact of various implementation techniques on time and storage efficiency, paying particularly close attention to the work-storage requirement of the two methods and their variants.

• Research Organization: Oak Ridge National Lab., TN (United States)
• Sponsoring Organization: DOE; USDOE, Washington, DC (United States)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 6097949
• Report Number(s): ORNL/TM-11960; ON: DE92004167
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
COMPUTERS
FACTORIZATION
MATHEMATICAL LOGIC
MATRICES
NUMERICAL SOLUTION
PERFORMANCE