Behavior of bivariate interpolation operators at points of discontinuity of the first kind

TL;DR

This paper introduces an index of convergence for double sequences to analyze how bivariate interpolation operators behave at points of discontinuity of the first kind, focusing on Lagrange and Shepard operators.

Contribution

It proposes a new convergence index to study the behavior of bivariate interpolation sequences at discontinuities, specifically for Lagrange and Shepard operators.

Findings

The index effectively characterizes convergence behavior at discontinuities.

Bivariate Lagrange and Shepard operators' behavior is described using the new index.

Results provide insights into the approximation properties near discontinuities.

Abstract

We introduce an index of convergence for double sequences of real numbers. This index is used to describe the behaviour of some bivariate interpolation sequences at points of discontinuity of the first kind. We consider in particular the case of bivariate Lagrange and Shepard operators.