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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
MathSciNet review: 1434942
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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

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

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