PHoMpara – Parallel Implementation of the Polyhedral Homotopy Continuation Method for Polynomial Systems

Authors:
T. Gunji;S. Kim;K. Fujisawa;M. Kojima
Affiliations:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, 152-8552, Tokyo, Meguro-ku, Japan;Department of Mathematics, Ewha Women's University, 11-1 Dahyun-dong, 120-750, Seoul, Sudaemoon-gu, Korea;Department of Mathematical Sciences, Tokyo Denki University, Ishizuka, 350-0394, Saitama, Hatoyama, Japan;Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, 152-8552, Tokyo, Meguro-ku, Japan
Venue:
Computing
Year:
2006

Citing 18
Cited 2

Optimal parallel algorithms for computing convex hulls and for sortng

Computing
Some examples for solving systems of algebraic equations by calculating groebner bases

Journal of Symbolic Computation
Integer and combinatorial optimization

Integer and combinatorial optimization
Coefficient-parameter polynomial continuation

Applied Mathematics and Computation
A neural network modeled by an adaptive Lotka-Volterra system

SIAM Journal on Applied Mathematics
A globally convergent parallel algorithm for zeros of polynomial systems

Non-Linear Analysis
Numerical continuation methods: an introduction

Numerical continuation methods: an introduction
A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots

Journal of Symbolic Computation
Computing singular solutions to polynomial systems

Advances in Applied Mathematics
Homotopies exploiting Newton polytopes for solving sparse polynomial systems

SIAM Journal on Numerical Analysis
A polyhedral method for solving sparse polynomial systems

Mathematics of Computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation

ACM Transactions on Mathematical Software (TOMS)
Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods

Applied Mathematics and Computation
Ninf: A Network Based Information Library for Global World-Wide Computing Infrastructure

HPCN Europe '97 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
Computing all nonsingular solutions of cyclic-n polynomial using polyhedral homotopy continuation methods

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
PHoM – a Polyhedral Homotopy Continuation Method for Polynomial Systems

Computing
Numerical Stability of Path Tracing in Polyhedral Homotopy Continuation Methods

Computing
Algorithm 857: POLSYS_GLP—a parallel general linear product homotopy code for solving polynomial systems of equations

ACM Transactions on Mathematical Software (TOMS)

HOM4PS-2.0para: Parallelization of HOM4PS-2.0 for solving polynomial systems

Parallel Computing
Polynomial homotopies on multicore workstations

Proceedings of the 4th International Workshop on Parallel and Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

The polyhedral homotopy continuation method is known to be a successful method for finding all isolated solutions of a system of polynomial equations. PHoM, an implementation of the method in C++, finds all isolated solutions of a polynomial system by constructing a family of modified polyhedral homotopy functions, tracing the solution curves of the homotopy equations, and verifying the obtained solutions. A software package PHoMpara parallelizes PHoM to solve a polynomial system of large size. Many characteristics of the polyhedral homotopy continuation method make parallel implementation efficient and provide excellent scalability. Numerical results include some large polynomial systems that had not been solved.