Some numerical applications of generalized Bernstein operators

Themistoclakis, Woula; OCCORSIO, Donatella; RUSSO, Maria Grazia

doi:10.33205/cma.868272

Some numerical applications of generalized Bernstein operators

DONATELLA OCCORSIO, (UNIVERSITY OF BASILICATA DEPARTMENT OF MATHEMATICS, COMPUTER SCIENCE AND ECONOMICS VIALE DELL’ATENEO LUCANO, 10, 85100, POTENZA, ITALY)

MARIA GRAZIA RUSSO, (UNIVERSITY OF BASILICATA DEPARTMENT OF MATHEMATICS, COMPUTER SCIENCE AND ECONOMICS VIALE DELL’ATENEO LUCANO, 10, 85100, POTENZA, ITALY)

WOULA THEMISTOCLAKIS (C.N.R. NATIONAL RESEARCH COUNCIL OF ITALY IAC INSTITUTE FOR APPLIED COMPUTING " MAURO PICONE" VIA P. CASTELLINO, 111, NAPLES, 80131, ITALY)

Constructive mathematical analysis (Online)

2 1

Yıl: 2021 Cilt: 4 Sayı: 2 Sayfa Aralığı: 186 - 214 Metin Dili: İngilizce DOI: 10.33205/cma.868272 İndeks Tarihi: 29-07-2022

Some numerical applications of generalized Bernstein operators

Öz:

In this paper, some recent applications of the so-called Generalized Bernstein polynomials are collected.This polynomial sequence is constructed by means of the samples of a continuous function f on equispaced points of[0, 1] and depends on an additional parameter which can be suitable chosen in order to improve the rate of convergenceto the function f, as the smoothness of f increases, overcoming the well-known low degree of approximation achievedby the classical Bernstein polynomials or by the piecewise polynomial approximation. The applications consideredhere deal with the numerical integration and the simultaneous approximation. Quadrature rules on equidistant nodesof [0, 1] are studied for the numerical computation of ordinary integrals in one or two dimensions, and usefully employed in Nyström methods for solving Fredholm integral equations. Moreover, the simultaneous approximationof the Hilbert transform and its derivative (the Hadamard transform) is illustrated. For all the applications, somenumerical details are given in addition to the error estimates, and the proposed approximation methods have beenimplemented providing numerical tests which confirm the theoretical estimates. Some open problems are also introduced.

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APA	OCCORSIO D, RUSSO M, Themistoclakis W (2021). Some numerical applications of generalized Bernstein operators. , 186 - 214. 10.33205/cma.868272
Chicago	OCCORSIO Donatella,RUSSO Maria Grazia,Themistoclakis Woula Some numerical applications of generalized Bernstein operators. (2021): 186 - 214. 10.33205/cma.868272
MLA	OCCORSIO Donatella,RUSSO Maria Grazia,Themistoclakis Woula Some numerical applications of generalized Bernstein operators. , 2021, ss.186 - 214. 10.33205/cma.868272
AMA	OCCORSIO D,RUSSO M,Themistoclakis W Some numerical applications of generalized Bernstein operators. . 2021; 186 - 214. 10.33205/cma.868272
Vancouver	OCCORSIO D,RUSSO M,Themistoclakis W Some numerical applications of generalized Bernstein operators. . 2021; 186 - 214. 10.33205/cma.868272
IEEE	OCCORSIO D,RUSSO M,Themistoclakis W "Some numerical applications of generalized Bernstein operators." , ss.186 - 214, 2021. 10.33205/cma.868272
ISNAD	OCCORSIO, Donatella vd. "Some numerical applications of generalized Bernstein operators". (2021), 186-214. https://doi.org/10.33205/cma.868272

APA	OCCORSIO D, RUSSO M, Themistoclakis W (2021). Some numerical applications of generalized Bernstein operators. Constructive mathematical analysis (Online), 4(2), 186 - 214. 10.33205/cma.868272
Chicago	OCCORSIO Donatella,RUSSO Maria Grazia,Themistoclakis Woula Some numerical applications of generalized Bernstein operators. Constructive mathematical analysis (Online) 4, no.2 (2021): 186 - 214. 10.33205/cma.868272
MLA	OCCORSIO Donatella,RUSSO Maria Grazia,Themistoclakis Woula Some numerical applications of generalized Bernstein operators. Constructive mathematical analysis (Online), vol.4, no.2, 2021, ss.186 - 214. 10.33205/cma.868272
AMA	OCCORSIO D,RUSSO M,Themistoclakis W Some numerical applications of generalized Bernstein operators. Constructive mathematical analysis (Online). 2021; 4(2): 186 - 214. 10.33205/cma.868272
Vancouver	OCCORSIO D,RUSSO M,Themistoclakis W Some numerical applications of generalized Bernstein operators. Constructive mathematical analysis (Online). 2021; 4(2): 186 - 214. 10.33205/cma.868272
IEEE	OCCORSIO D,RUSSO M,Themistoclakis W "Some numerical applications of generalized Bernstein operators." Constructive mathematical analysis (Online), 4, ss.186 - 214, 2021. 10.33205/cma.868272
ISNAD	OCCORSIO, Donatella vd. "Some numerical applications of generalized Bernstein operators". Constructive mathematical analysis (Online) 4/2 (2021), 186-214. https://doi.org/10.33205/cma.868272