Exploiting the memory hierarchy in sequential and parallel sparse Cholesky factorization

Technical Report · Sun Nov 01 04:00:00 EST 1992

OSTI ID:6363278

Rothberg, E

Cholesky factorization of large sparse matrices is an extremely important computation, arising in a wide range of domains including linear programming, finite element analysis, and circuit simulation. This thesis investigates crucial issues for obtaining high performance for this computation on sequential and parallel machines with hierarchical memory systems. The thesis begins by providing the first thorough analysis of the interaction between sequential sparse Cholesky factorization methods and memory hierarchies. The authors look at popular existing methods and find that they produce relatively poor memory hierarchy performance. The methods are extended, using blocking techniques, to reuse data in the fast levels of the memory hierarchy. This increased reuse is shown to provide a three-fold speedup over popular existing approaches (e.g., SPARSPAK) on modem workstations. The thesis then considers the use of blocking techniques in parallel sparse factorization. The authors first describe parallel methods we have developed that are natural extensions of the sequential approach described above. These methods distribute panels (sets of contiguous columns with nearly identical non-zero structures) among the processors. The thesis shows that for small parallel machines, the resulting methods again produce substantial performance improvements over existing methods. A framework is provided for understanding the performance of these methods, and also for understanding the limitations inherent in them. Using this framework, the thesis shows that panel methods are inappropriate for large-scale parallel machines because they do not expose enough concurrency.... Hierarchical-memory machines, Sparse Cholesky factorization, Parallel processing.

• Research Organization: Stanford Univ., CA (United States). Dept. of Computer Science
• OSTI ID: 6363278
• Report Number(s): AD-A-262849/3/XAB; STAN-CS--92-1459; CNN: N00039-91-C-0138; N00014-87-K-0828
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ARRAY PROCESSORS
CALCULATION METHODS
COUNTING TECHNIQUES
DECISION MAKING
ELECTRONIC CIRCUITS
FACTORIZATION
FINITE ELEMENT METHOD
LINEAR PROGRAMMING
MATRICES
MATRIX ELEMENTS
MEMORY MANAGEMENT
NUMERICAL SOLUTION
PARALLEL PROCESSING
PROGRAMMING
SEQUENTIAL CIRCUITS
SEQUENTIAL SCANNING