On simple double zeros and badly conditioned zeros of analytic functions of variables

Authors:
Jean-Pierre Dedieu and Mike Shub

Journal:
Math. Comp. **70** (2001), 319-327

MSC (2000):
Primary 65H10

DOI:
https://doi.org/10.1090/S0025-5718-00-01194-7

Published electronically:
March 1, 2000

MathSciNet review:
1680867

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We give a numerical criterion for a badly conditioned zero of a system of analytic equations to be part of a cluster of two zeros.

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Additional Information

**Jean-Pierre Dedieu**

Affiliation:
Laboratoire Approximation et Optimisation, Université Paul Sabatier, 31062 Toulouse Cedex 04, France

Email:
dedieu@cict.fr

**Mike Shub**

Affiliation:
IBM T.J. Watson Research Center, Yorktowns Heights, New York 10598-0218

Email:
mshub@us.ibm.com

DOI:
https://doi.org/10.1090/S0025-5718-00-01194-7

Keywords:
Systems of equations,
multiple zeros,
condition numbers

Received by editor(s):
January 12, 1999

Published electronically:
March 1, 2000

Additional Notes:
This work was done while both authors were at MSRI, Berkeley, in fall 1998, for the Foundations of Computational Mathematics program.

Partially supported by the National Science Foundation

Article copyright:
© Copyright 2000
American Mathematical Society