On a conjecture concerning interpolation by bivariate Bernstein polynomials

dc.date.accessioned	2024-02-14T18:06:05Z
dc.date.created	2023-06-30T12:50:54Z
dc.date.issued	2023
dc.identifier.citation	Floater, Michael S. . On a conjecture concerning interpolation by bivariate Bernstein polynomials. Journal of Approximation Theory. 2023, 293
dc.identifier.uri	http://hdl.handle.net/10852/108064
dc.description.abstract	In this paper we discuss a conjecture of Schumaker that the principal submatrices of collocation matrices of bivariate Bernstein polynomials over triangular grids have positive determinant. It is easy to show that the conjecture holds for the 2 × 2 submatrices. In this paper we show that it also holds for the 3 × 3 submatrices, working with the equivalent ‘monomial form’ of the conjecture. This result generalizes to a class of 3 × 3 matrices which will be described.
dc.language	EN
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.uri	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.title	On a conjecture concerning interpolation by bivariate Bernstein polynomials
dc.type	Journal article
dc.creator.author	Floater, Michael S.
dc.date.embargoenddate	2025-06-01
cristin.unitcode	185,15,13,0
cristin.unitname	Matematisk institutt
cristin.ispublished	true
cristin.qualitycode	1
dc.identifier.cristin	2159857
dc.identifier.bibliographiccitation	info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal of Approximation Theory&rft.volume=293&rft.spage=&rft.date=2023
dc.identifier.jtitle	Journal of Approximation Theory
dc.identifier.volume	293
dc.identifier.pagecount	0
dc.identifier.doi	https://doi.org/10.1016/j.jat.2023.105920
dc.type.document	Tidsskriftartikkel
dc.type.peerreviewed	Peer reviewed
dc.source.issn	0021-9045
dc.type.version	AcceptedVersion
cristin.articleid	105920