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Andrew R. Conn (arconnwatson.ibm.com) Abstract: We show how to derive error estimates between a function and its interpolating polynomial and between their corresponding derivatives. The derivation is based on a new definition of wellpoisedness for the interpolation set, directly connecting the accuracy of the error estimates with the geometry of the points in the set. This definition is equivalent to the boundedness of Lagrange polynomials, but it provides new geometric intuition. Our approach extracts the error bounds for all of the derivatives using the same analysis; the error bound for the function values is then derived a posteriori. We also develop an algorithm to build a set of wellpoised interpolation points or to modify an existing set to ensure its wellpoisedness. We comment on the optimal geometries corresponding to the best possible wellpoised sets in the case of linear interpolation. Keywords: multivariate polynomial interpolation, error estimates, poisedness, derivativefree optimization Category 1: Nonlinear Optimization (Other ) Category 2: Applications  Science and Engineering Citation: Preprint 0309, Department of Mathematics, University of Coimbra, Portugal, April 2003 Download: [Postscript] Entry Submitted: 05/03/2003 Modify/Update this entry  
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