Approximation and interpolation with Bernstein polynomials.

Allen, Larry J., 1993-

Approximation and interpolation with Bernstein polynomials.

dc.contributor.advisor	Kirby, Robert C.
dc.creator	Allen, Larry J., 1993-
dc.date.accessioned	2022-01-28T14:48:23Z
dc.date.available	2022-01-28T14:48:23Z
dc.date.created	2021-12
dc.date.issued	2021-11-03
dc.date.submitted	December 2021
dc.date.updated	2022-01-28T14:48:24Z
dc.description.abstract	Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. In this dissertation, we investigate fundamental problems in approximation theory and numerical analysis involving Bernstein polynomials. We begin by developing a structured decomposition of the inverse of the matrices related to approximation and interpolation. These matrices are highly ill-conditioned, and so we introduce a nonstandard matrix norm to study the conditioning of the matrices, showing that the conditioning in this case is better than in the standard 2-norm. We conclude by giving an algorithm for enforcing bounds constraints on the approximating polynomial. Extensions of the interpolation problem and constrained approximation problem to higher dimensions are also considered.
dc.format.mimetype	application/pdf
dc.identifier.uri	https://hdl.handle.net/2104/11716
dc.language.iso	en
dc.rights.accessrights	Worldwide access
dc.subject	Bernstein polynomials. Lagrange polynomials. Legendre polynomials. Bernstein mass matrix. Bernstein-Vandermonde matrix. Matrix inverse. Bezout matrix. Hankel matrix. Toeplitz matrix. Interpolation. Constrained optimization. Spectral decomposition. Fast algorithm. Conditioning.
dc.title	Approximation and interpolation with Bernstein polynomials.
dc.type	Thesis
dc.type.material	text
thesis.degree.department	Baylor University. Dept. of Mathematics.
thesis.degree.grantor	Baylor University
thesis.degree.level	Doctoral
thesis.degree.name	Ph.D.