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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Numerical Analysis and Scientific Computation
Volume 10 - 2024 | doi: 10.3389/fams.2024.1489137
This article is part of the Research Topic Approximation Methods and Analytical Modeling Using Partial Differential Equations View all 18 articles

A Boolean sum interpolation for multivariate functions of bounded variation

Provisionally accepted
Yevgeniya V. Semenova Yevgeniya V. Semenova 1*Jürgen Prestin Jürgen Prestin 2
  • 1 Institute of Mathematics (NAN Ukraine), Kyiv, Ukraine
  • 2 Institute of Mathematics, University of Lübeck, Lübeck, Schleswig-Holstein, Germany

The final, formatted version of the article will be published soon.

    In this paper we study the approximation error for trigonometric interpolation of multivariate functions with bounded variation. We employ the notation introduced in \cite{AIS_PAUS_SV_TIC_2017} for the so-called Hardy-Krause variation. In addition to the interpolation on the tensor product grid, we discuss in particular the $L_p$ error of the interpolation on sparse grids for such functions of bounded variation.

    Keywords: Boolean sum operator, multivariate function of bounded variation, Interpolation problem, Sparse grid, Tensor product grid

    Received: 31 Aug 2024; Accepted: 02 Oct 2024.

    Copyright: © 2024 Semenova and Prestin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Yevgeniya V. Semenova, Institute of Mathematics (NAN Ukraine), Kyiv, Ukraine

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