Luis Vicente, Department of Mathematics, University of Coimbra, Portugal, IBM T.J. Watson Research Center, Yorktown Heights, New York.
"Error estimates and poisedness in multivariate polynomial interpolation and derivative-free optimization"
The purpose of this talk is twofold. We show first how to derive error estimates between a function and its interpolating polynomial and between their corresponding derivatives. The derivation is based on a new concept of well-poisedness for the interpolation set, directly connecting the accuracy of the error estimates with the geometry of the points in the set. The prior existing error estimates make use of less intuitive geometrical conditions. In the other part of the talk, we will briefly describe derivative-free optimization techniques based on geometrical concepts like well-poisedness and positive bases, pointing out what are the key ingredients for convergence and making a link to the first part of the talk.
TUESDAY, October 29, 2002