## 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.## References

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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