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Mathematics of Computation

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

Authors: Jean-Pierre Dedieu and Mike Shub
Journal: Math. Comp. 70 (2001), 319-327
MSC (2000): Primary 65H10
Published electronically: March 1, 2000
MathSciNet review: 1680867
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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

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

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