Sparse cholesky factorization on a simulated hypercube

Authors:
Venu M. Padakanti
Affiliations:
Old Dominion University, Norfolk, VA
Venue:
ACM-SE 30 Proceedings of the 30th annual Southeast regional conference
Year:
1992

Citing 4
Cited 0

Computational models and task scheduling for parallel sparse Cholesky factorization

Parallel Computing
Sparse Cholesky factorization on a local-memory multiprocessor

SIAM Journal on Scientific and Statistical Computing
The algebraic eigenvalue problem

The algebraic eigenvalue problem
Computer Solution of Large Sparse Positive Definite

Computer Solution of Large Sparse Positive Definite

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Abstract

Solutions to large systems of linear equations are used in a wide range of problems. Many of these systems can be represented by symmetric sparse positive definite matrices, and the Cholesky decomposition has been proved to be one of the best methods for solving symmetric positive definite matrices. Our work deals with the parallel Cholesky decomposition of such matrices and their implementation on a simulated hypercube. We decompose the solution into subtasks that have precedence relations among themselves. These precedence relations are expressed in the form of an elimination tree where each node represents a subtask assigned to a processor for execution. The scheduling of these tasks is based on the Highest Level First policy which has been proved to be an optimal one in case of static and deterministic scheduling. A flexible hypercube simulator is developed in C language under UNIX environment. The simulation studies indicate that this algorithm is very efficient for large and well ordered matrices.