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

Content Provider	ACM Digital Library
Author	Sosonkina, Masha Su, Hai-Jun Mccarthy, J. Michael Watson, Layne T.
Copyright Year	2006
Abstract	Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked and handling singular solutions have made probability-one homotopy methods even more practical. POLSYS_GLP consists of Fortran 95 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used on a distributed memory multiprocessor in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 95-derived data types and MPI to support a general linear product (GLP) polynomial system structure. GLP structure is intermediate between the partitioned linear product structure used by POLSYS_PLP (Algorithm 801) and the BKK-based structure used by PHCPACK. The code requires a GLP structure as input, and although finding the optimal GLP structure is a difficult combinatorial problem, generally physical or engineering intuition about a problem yields a very good GLP structure. POLSYS_GLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different GLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.
Starting Page	561
Ending Page	579
Page Count	19
File Format	PDF
ISSN	00983500
e-ISSN	15577295
DOI	10.1145/1186785.1186789
Volume Number	32
Issue Number	4
Journal	ACM Transactions on Mathematical Software (TOMS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2006-12-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chow-Yorke algorithm Fortran 95 Curve tracking Fixed point General linear product Globally convergent Homotopy methods Linear product decomposition Probability-one Zero
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Software

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Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations

Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms

Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms

Note on the end game in homotopy zero curve tracking

Solving Galerkin Approximations to Nonlinear Two-Point Boundary Value Problems by a Globally Convergent Homotopy Method

Numerical Linear Algebra Aspects of Globally Convergent Homotopy Methods

Preconditioned Iterative Methods for Homotopy Curve Tracking

Solving Finite Difference Approximations to Nonlinear Two-Point Boundary Value Problems by a Homotopy Method

Experiments with Conjugate Gradient Algorithms for Homotopy Curve Tracking

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

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Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations

Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms

Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms

Note on the end game in homotopy zero curve tracking

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