Work

On the Lebesgue Constant of the Morrow–Patterson Points

Year: 2025

Type: article

Abstract: The study of interpolation nodes and their associated Lebesgue constants is 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 $${\mathcal {O}}(n^2)$$ O ( n 2 ) as was conjectured based on numerical evidence about 20 years ago in the paper by Caliari et al. (Appl Math Comput 165(2):261–274, 2005).

Source: Constructive Approximation

DOI: 10.1007/s00365-025-09710-x

Authors: Tomasz Beberok, Leokadia Bialas-Ciez, Stefano De Marchi

Institutions: University of Agriculture in Krakow, Jagiellonian University, University of Padua

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Padova, Gruppo Nazionale per il Calcolo Scientifico