Numerical Calculation of the Multiplicity
of a Solution to Algebraic Equations
Authors:
Hidetsune Kobayashi, Hideo Suzuki and Yoshihiko Sakai
Journal:
Math. Comp. 67 (1998), 257-270
MSC (1991):
Primary 14Q99, 65H10; Secondary 14N05, 65H20
DOI:
https://doi.org/10.1090/S0025-5718-98-00906-5
MathSciNet review:
1434942
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Abstract | References | Similar Articles | Additional Information
Abstract: A method to calculate numerically the multiplicity of a solution to a system of algebraic equations is presented. The method is an application of Zeuthen's rule which gives the multiplicity of a solution as the multiplicity of a united point of an algebraic correspondence defined naturally by the system. The numerical calculation is applicable to a large scale system of algebraic equations which may have a solution that we cannot calculate the multiplicity by a symbolic computation.
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Additional Information
Hidetsune Kobayashi
Affiliation:
Department of Mathematics, Nihon University, 1-8 Kanda-surugadai, Tokyo 101, Japan
Email:
hikoba@math.cst.nihon-u.ac.jp
Hideo Suzuki
Affiliation:
Tokyo Polytechnic College, 2-32-1 Ogawa-nishi Kodaira, Tokyo, Japan
Yoshihiko Sakai
Affiliation:
Visual Science Laboratory, Inc., 2-21 Kanda-awajicho, Chiyoda, Tokyo, Japan
Email:
sakai@vsl.co.jp
DOI:
https://doi.org/10.1090/S0025-5718-98-00906-5
Keywords:
Multiplicity,
Zeuthen's rule,
homotopy method,
system of algebraic equations
Received by editor(s):
July 13, 1995
Received by editor(s) in revised form:
August 28, 1996
Article copyright:
© Copyright 1998
American Mathematical Society
