Title page for ETD etd-72598-142819

Type of Document Master's Thesis
Author Wise, Steven Matthew
Author's Email Address stwise@seneca.cs.vt.edu
URN etd-72598-142819
Title POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Watson, Layne T. Committee Chair
Beattie, Christopher A. Committee Member
Rossi, John F. Committee Member
  • Numerical Analysis
  • Homotopy Methods
  • Polynomial Systems of Equations
  • Zeros.
Date of Defense 1998-08-20
Availability unrestricted
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 in the handling of

singular solutions, have made probability-one homotopy

methods even more practical. This thesis describes the

theory behind and performance of the new code POLSYS_PLP,

which consists of Fortran 90 modules for finding all

isolated solutions of a complex coefficient polynomial

system of equations by a probability-one homotopy method.

The package is intended to be used in conjunction with

HOMPACK90, and makes extensive use of Fortran 90 derived

data types to support a partitioned linear product (PLP)

polynomial system structure. PLP structure is a

generalization of m-homogeneous structure, whereby each

component of the system can have a different m-homogeneous

structure. POLSYS_PLP 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 PLP structures and their

corresponding Bezout numbers can be systematically explored

before committing to root finding.

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