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Generalized Popoviciu Expansions for Bernstein Polynomials of a Rational Module

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dc.contributor.authorTikhonov, I. V.
dc.contributor.authorTsvetkovich, D. G.
dc.contributor.authorSherstyukov, V. B.
dc.date.accessioned2024-12-25T15:16:35Z
dc.date.available2024-12-25T15:16:35Z
dc.date.issued2022
dc.description.abstract© 2022, Springer Science+Business Media, LLC, part of Springer Nature.We study Bernstein polynomials for simple nonsmooth rational module functions. We show that these polynomials can be represented as special sums of regular structure. For historical reasons, the representations found are naturally called “generalized Popoviciu expansions.” To write generalized expansions, we develop a special formalism based on combinatorial calculations. Based on the formulas obtained, we propose a complete description of the character of convergence of the Bernstein polynomials studied in the complex plane. We also discuss the relationship of generalized Popoviciu expansions with the distribution of zeros of Bernstein polynomials. In the final part of the paper, we present additional new relations for Bernstein polynomials of the rational module function.
dc.format.extentС. 532-578
dc.identifier.citationTikhonov, I. V. Generalized Popoviciu Expansions for Bernstein Polynomials of a Rational Module / Tikhonov, I.V., Tsvetkovich, D.G., Sherstyukov, V.B. // Journal of Mathematical Sciences (United States). - 2022. - 263. - № 4. - P. 532-578. - 10.1007/s10958-022-05948-z
dc.identifier.doi10.1007/s10958-022-05948-z
dc.identifier.urihttps://www.doi.org/10.1007/s10958-022-05948-z
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85132191511&origin=resultslist
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/28074
dc.relation.ispartofJournal of Mathematical Sciences (United States)
dc.titleGeneralized Popoviciu Expansions for Bernstein Polynomials of a Rational Module
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue4
oaire.citation.volume263
relation.isOrgUnitOfPublicationd19559ab-04cd-486a-ae8e-f40ccd36a1a6
relation.isOrgUnitOfPublication.latestForDiscoveryd19559ab-04cd-486a-ae8e-f40ccd36a1a6
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