On the Lebesgue Constant of the Morrow–Patterson Points

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 $${\mathcal {O}}(n^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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).