Concurrent function evaluations in local and global optimization
Computer Methods in Applied Mechanics and Engineering
Algorithms for matrix transposition on Boolean N-cube configured ensemble architecture
SIAM Journal on Matrix Analysis and Applications
Granularity issues for solving polynomial systems via globally convergent algorithms on a hypercube
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
QR factorization of a dense matrix on a hypercube multiprocessor
SIAM Journal on Scientific and Statistical Computing
A globally convergent parallel algorithm for zeros of polynomial systems
Non-Linear Analysis
Preconditioned iterative methods for homotopy curve tracking
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
Algorithm 596: a program for a locally parameterized
ACM Transactions on Mathematical Software (TOMS)
The Granularity of Homotopy Algorithms for Polynomial Systems of Equations
Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing
Parallel Homotopy Curve Tracking on a Hypercube
Proceedings of the Fourth SIAM Conference on Parallel Processing for Scientific Computing
Solution of Nonlinear Least-Square Problems on a Multiprocessor
Solution of Nonlinear Least-Square Problems on a Multiprocessor
QR Factorization Algorithms for Coarse-Grained Distributed Systems
QR Factorization Algorithms for Coarse-Grained Distributed Systems
ACM Transactions on Mathematical Software (TOMS)
Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm
International Journal of Computational Science and Engineering
Parallel homotopy algorithms to solve polynomial systems
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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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.