A nonlinear parallel algorithm with application to the Stefan problem
SIAM Journal on Numerical Analysis
Parallel algorithms for nonlinear problems
SIAM Journal on Algebraic and Discrete Methods
Algorithm 502: Dependence of Solution of Nonlinear Systems on a Parameter [C5]
ACM Transactions on Mathematical Software (TOMS)
Algorithm 555: Chow-Yorke Algorithm for Fixed Points or Zeros of C2 Maps [C5]
ACM Transactions on Mathematical Software (TOMS)
Algorithm 596: a program for a locally parameterized
ACM Transactions on Mathematical Software (TOMS)
Message Length Effects for Solving Polynomial Systems on a Hypercube
Message Length Effects for Solving Polynomial Systems on a Hypercube
Globally Convergent Parallel Algorithm for Zeros of Polynomial Systems
Globally Convergent Parallel Algorithm for Zeros of Polynomial Systems
What have we learnt from using real parallel machines to solve real problems?
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
Parallel unit tangent vector computation for homotopy curve tracking on a hypercube
CSC '90 Proceedings of the 1990 ACM annual conference on Cooperation
The Parallel Complexity of Embedding Algorithms for the Solution of Systems of Nonlinear Equations
IEEE Transactions on Parallel and Distributed Systems
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Polynomial systems of equations frequently arise in many applications such as solid modelling, robotics, computer vision, chemistry, chemical engineering, and mechanical engineering. Locally convergent iterative methods such as quasi-Newton methods may diverge or fail to find all meaningful solutions of a polynomial system. Recently a homotopy algorithm has been proposed for polynomial systems that is guaranteed globally convergent (always converges from an arbitrary starting point) with probability one, finds all solutions to the polynomial system, and has a large amount of inherent parallelism. There are several ways the homotopy algorithms can be decomposed to run on a hypercube. The granularity of a decomposition has a profound effect on the performance of the algorithm. The results of decompositions with two different granularities are presented. The experiments were conducted on an iPSC-16 hypercube using actual industrial problems.