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Mathematics of Computation

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Multihomogeneous Newton methods

Authors: Jean-Pierre Dedieu and Mike Shub
Journal: Math. Comp. 69 (2000), 1071-1098
MSC (1991): Primary 65H10, 15A99
Published electronically: March 10, 1999
MathSciNet review: 1752092
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Abstract: We study multihomogeneous analytic functions and a multihomogeneous Newton's method for finding their zeros. We give a convergence result for this iteration and we study two examples: the evaluation map and the generalized eigenvalue problem.

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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, Yorktown Heights, NY 10598-0218, USA

Received by editor(s): October 16, 1997
Received by editor(s) in revised form: July 22, 1998
Published electronically: March 10, 1999
Additional Notes: This paper was completed when the first author was visiting at the IBM T.J. Watson Research Center in August 1997.
The second author was partially supported by an NSF grant
Article copyright: © Copyright 2000 American Mathematical Society