The parallel complexity of embedding algorithms for the solution of systems of nonlinear equations

Journal Article · Thu Apr 01 04:00:00 EST 1993 · IEEE Transactions on Parallel and Distributed Systems (Institute of Electrical and Electronics Engineers); (United States)

DOI:https://doi.org/10.1109/71.219760· OSTI ID:6437728

Chakraborty, A ^[1]; Allison, D C.S.; Ribbens, C J; Watson, L T ^[2]

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1. Citibank, New York, NY (United States)
2. Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Computer Science

Embedding algorithms for nonlinear systems of equations construct a continuous family of systems, and solve the given system by tracking the continuous curve of solutions to the family. Solving nonlinear equations by a globally convergent embedding algorithm requires the evaluation and factoring of a Jacobian matrix at many points along the embedding curve. This paper describes how to optimize the evaluation of the Jacobian matrix on a hypercube. Several static and dynamic strategies for assigning components of the Jacobian to processors on the hypercube are investigated, and it is found that a static rectangular grid mapping is the preferred choice for inclusion in a robust parallel mathematical software package. The static linear mapping is a viable alternative when there are many common subexpressions in the component evaluation, while the dynamic assignment strategy should only be considered when there is large variation in the evaluation times for the components, leading to a load imbalance on the processors.

• DOE Contract Number: FG05-88ER25068
• OSTI ID: 6437728
• Journal Information: IEEE Transactions on Parallel and Distributed Systems (Institute of Electrical and Electronics Engineers); (United States), Journal Name: IEEE Transactions on Parallel and Distributed Systems (Institute of Electrical and Electronics Engineers); (United States) Vol. 4:4; ISSN ITDSEO; ISSN 1045-9219
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
COMPUTERS
CONVERGENCE
FUNCTIONS
HYPERCUBE COMPUTERS
JACOBIAN FUNCTION
MATHEMATICAL LOGIC
MATRICES
NONLINEAR PROBLEMS
OPTIMIZATION
PARALLEL PROCESSING
PROGRAMMING