AUTHOR=Prestin Jürgen , Semenova Yevgeniya V. 

TITLE=A Boolean sum interpolation for multivariate functions of bounded variation

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1489137

DOI=10.3389/fams.2024.1489137

ISSN=2297-4687

ABSTRACT=<p>This paper deals with the approximation error of trigonometric interpolation for multivariate functions of bounded variation in the sense of Hardy-Krause. We propose interpolation operators related to both the tensor product and sparse grids on the multivariate torus. For these interpolation processes, we investigate the corresponding error estimates in the <italic>L</italic><sub><italic>p</italic></sub> norm for the class of functions under consideration. In addition, we compare the accuracy with the cardinality of these grids in both approaches.</p>