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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Numerical calculation of the multiplicity of a solution to algebraic equations
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by Hidetsune Kobayashi, Hideo Suzuki and Yoshihiko Sakai PDF
Math. Comp. 67 (1998), 257-270 Request permission

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
  • Received by editor(s): July 13, 1995
  • Received by editor(s) in revised form: August 28, 1996
  • © Copyright 1998 American Mathematical Society
  • 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