On the Lebesgue constant of the Morrow-Patterson points

2024/12/19 by Tomasz Beberok, Beberok, Tomasz, Leokadia Białas-Cież +3
Economics, Econometrics and Finance · Mathematics · Computer Science · #Stochastic processes and financial applications #Advanced Optimization Algorithms Research #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2412.14595

Abstract

The study of interpolation nodes and their associated Lebesgue constants are central to numerical analysis, impacting the stability and accuracy of polynomial approximations. In this paper, we will explore the Morrow-Patterson points, a set of interpolation nodes introduced to construct cubature formulas of a minimum number of points in the square for a fixed degree n. We prove that their Lebesgue constant growth is \cal O(n²) as was conjectured based on numerical evidence about twenty years ago in the paper by Caliari, M., De Marchi, S., Vianello, M., \it Bivariate polynomial interpolation on the square at new nodal sets, Appl. Math. Comput. 165(2) (2005), 261--274.

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