DocumentCode :
914509
Title :
The parallel complexity of embedding algorithms for the solution of systems of nonlinear equations
Author :
Chakraborty, Amal ; Allison, Donald C S ; Ribbens, Calvin J. ; Watson, Layne T.
Author_Institution :
Citibank, New York, NY, USA
Volume :
4
Issue :
4
fYear :
1993
fDate :
4/1/1993 12:00:00 AM
Firstpage :
458
Lastpage :
465
Abstract :
Embedding algorithms used to solve nonlinear systems of equations do so by constructing a continuous family of systems and solving 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. Ways to optimize the Jacobian matrix on a hypercube are described. Several static and dynamical strategies for assigning components of the Jacobian to processors on the hypercube are investigated. 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, and 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
Keywords :
computational complexity; nonlinear equations; parallel algorithms; Jacobian matrix; dynamic assignment; embedding algorithms; hypercube; mathematical software package; nonlinear equations; parallel complexity; static rectangular grid mapping; Algorithm design and analysis; Concurrent computing; Hypercubes; Jacobian matrices; Linear algebra; Newton method; Nonlinear equations; Nonlinear systems; Robustness; Software packages;
fLanguage :
English
Journal_Title :
Parallel and Distributed Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
1045-9219
Type :
jour
DOI :
10.1109/71.219760
Filename :
219760
Link To Document :
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