Type of Document Master's Thesis Author Wise, Steven Matthew Author's Email Address email@example.com 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 Keywords
- Numerical Analysis
- Homotopy Methods
- Polynomial Systems of Equations
Date of Defense 1998-08-20 Availability unrestricted AbstractGlobally 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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