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
Full-text PDF Free Access
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.
- J. S. Semple and L. Roth : Introduction to Algebraic Geometry, Oxford Science Publications, Clarendon Press, Oxford, 1949.
- B. L. van der Waerden, Einführung in die algebraische Geometrie, Springer-Verlag, Berlin-New York, 1973 (German). Zweite Auflage; Die Grundlehren der mathematischen Wissenschaften, Band 51. MR 0344245
- H. Kobayashi, H. Suzuki and Y. Sakai: Separation of close roots by linear fractional transformation, Proc. of ASCM, 1-10, Scientists INC, 1995.
- William Fulton, Algebraic curves. An introduction to algebraic geometry, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes written with the collaboration of Richard Weiss; Mathematics Lecture Notes Series. MR 0313252
- Alden H. Wright, Finding all solutions to a system of polynomial equations, Math. Comp. 44 (1985), no. 169, 125–133. MR 771035, DOI https://doi.org/10.1090/S0025-5718-1985-0771035-4
Retrieve articles in Mathematics of Computation with MSC (1991): 14Q99, 65H10, 14N05, 65H20
Retrieve articles in all journals with MSC (1991): 14Q99, 65H10, 14N05, 65H20
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
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
