NDLI: Finding all isolated solutions to polynomial systems using HOMPACK

Content Provider	ACM Digital Library
Author	Sommese, Andrew J. Morgan, Alexander P. Watson, Layne T.
Copyright Year	1989
Abstract	Although the theory of polynomial continuation has been established for over a decade (following the work of Garcia, Zangwill, and Drexler), it is difficult to solve polynomial systems using continuation in practice. Divergent paths (solutions at infinity), singular solutions, and extreme scaling of coefficients can create catastrophic numerical problems. Further, the large number of paths that typically arise can be discouraging. In this paper we summarize polynomial-solving homotopy continuation and report on the performance of three standard path-tracking algorithms (as implemented in HOMPACK) in solving three physical problems of varying degrees of difficulty. Our purpose is to provide useful information on solving polynomial systems, including specific guidelines for homotopy construction and parameter settings. The $\textit{m}-homogeneous$ strategy for constructing polynomial homotopies is outlined, along with more traditional approaches. Computational comparisons are included to illustrate and contrast the major HOMPACK options. The conclusions summarize our numerical experience and discuss areas for future research.
Starting Page	93
Ending Page	122
Page Count	30
File Format	PDF
ISSN	00983500
e-ISSN	15577295
DOI	10.1145/63522.64124
Volume Number	15
Issue Number	2
Journal	ACM Transactions on Mathematical Software (TOMS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1989-06-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Software

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