Total positivity and high relative accuracy for a generalized Bernstein basis

Jorge Delgado, Héctor Orera and J.M. Peña

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 490-509

Abstract: The Bernstein basis of polynomials was generalized in Khosravian-Arabet al. (2018) in order to achieve better approximations than with classical Bernstein polynomials. We consider a family of those bases and prove their total positivity, which is very convenient in computer aided design. For adequate parameter values, we also obtain a subtraction-free algorithm for the bidiagonal decomposition of the corresponding collocation matrices, which allows us to derive accurate algorithms to compute all eigenvalues, all singular values or the inverse of such matrices. Numerical experiments confirm the high accuracy of our method.

Keywords: Generalized Bernstein bases; Total positivity; Accurate computations (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:490-509

DOI: 10.1016/j.matcom.2026.05.029

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