{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:47:20Z","timestamp":1753890440571,"version":"3.41.2"},"reference-count":19,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T00:00:00Z","timestamp":1729468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats: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 <jats:italic>L<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub> norm for the class of functions under consideration. In addition, we compare the accuracy with the cardinality of these grids in both approaches.<\/jats:p>","DOI":"10.3389\/fams.2024.1489137","type":"journal-article","created":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T04:36:56Z","timestamp":1729485416000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A Boolean sum interpolation for multivariate functions of bounded variation"],"prefix":"10.3389","volume":"10","author":[{"given":"J\u00fcrgen","family":"Prestin","sequence":"first","affiliation":[]},{"given":"Yevgeniya V.","family":"Semenova","sequence":"additional","affiliation":[]}],"member":"1965","published-online":{"date-parts":[[2024,10,21]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1017\/S0305004116000633","article-title":"On functions of bounded variation","volume":"162","author":"Aistleitner","year":"2017","journal-title":"Math Proc Cambr Philos Soc"},{"key":"B2","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-030-04306-3","article-title":"Numerical Fourier analysis (Cham: Birkh\u00e4user)","volume":"30","author":"Plonka","year":"2018","journal-title":"Appl Numer Harmon Anal"},{"key":"B3","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1007\/BF01058914","article-title":"Approximation of periodic functions by interpolation polynomials in L1","volume":"42","author":"Motornyi","year":"1990","journal-title":"Ukr Math J"},{"key":"B4","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1006\/jath.1994.1037","article-title":"Convergence rate for trigonometric interpolation of non-smooth functions","volume":"77","author":"Prestin","year":"1994","journal-title":"J Approx Theory"},{"key":"B5","first-page":"195","article-title":"Eine Bemerkung zur trigonometrischen Interpolation","volume":"9","author":"Zacharias","year":"1981","journal-title":"Beitr Numer Math"},{"key":"B6","first-page":"699","article-title":"Trigonometric interpolation of functions of bounded variation","volume":"1984","author":"Prestin","year":"1984","journal-title":"Constr Theor Funct"},{"key":"B7","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1090\/S0002-9947-1933-1501718-2","article-title":"On definitions of bounded variation for functions of two variables","volume":"35","author":"Clarkson","year":"1933","journal-title":"Trans Amer MathSoc"},{"volume-title":"Bounded Variation and Around. 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