Transcendental bernstein series: Interpolation and approximation

Z. Avazzadeh; H. Hassani; J. A. Tenreiro Machado; P. Agarwal; E. Naraghirad

Transcendental bernstein series: Interpolation and approximation

Z. Avazzadeh
, H. Hassani
, J. A. Tenreiro Machado
, P. Agarwal
, E. Naraghirad

University of South Africa
International College of Engineering
Polytechnic of Porto
Yasouj University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This paper adopts the transcendental Bernstein series (TBS), a set of basis functions based on the Bernstein polynomials (BP), for approximating analytical functions. The TBS is more accurate than the BP method, particularly in approximating functions including one or more transcendental terms. The numerical results reveal also the applicability and higher computational efficiency of the new approach.

Original language	English
Title of host publication	Advances in Special Functions of Fractional Calculus
Subtitle of host publication	Special Functions in Fractional Calculus and Their Applications in Engineering
Publisher	Bentham Science Publishers
Pages	73-93
Number of pages	21
ISBN (Electronic)	9789815079333
ISBN (Print)	9789815079340
State	Published - 11 Apr 2023
Externally published	Yes

Keywords

Bernstein polynomials
Transcendental Bernstein series
Transcendental functions

Cite this

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title = "Transcendental bernstein series: Interpolation and approximation",

abstract = "This paper adopts the transcendental Bernstein series (TBS), a set of basis functions based on the Bernstein polynomials (BP), for approximating analytical functions. The TBS is more accurate than the BP method, particularly in approximating functions including one or more transcendental terms. The numerical results reveal also the applicability and higher computational efficiency of the new approach.",

keywords = "Bernstein polynomials, Transcendental Bernstein series, Transcendental functions",

author = "Z. Avazzadeh and H. Hassani and \{Tenreiro Machado\}, \{J. A.\} and P. Agarwal and E. Naraghirad",

year = "2023",

month = apr,

day = "11",

language = "English",

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pages = "73--93",

booktitle = "Advances in Special Functions of Fractional Calculus",

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Transcendental bernstein series: Interpolation and approximation. / Avazzadeh, Z.; Hassani, H.; Tenreiro Machado, J. A. et al.
Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering. Bentham Science Publishers, 2023. p. 73-93.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Transcendental bernstein series

T2 - Interpolation and approximation

AU - Avazzadeh, Z.

AU - Hassani, H.

AU - Tenreiro Machado, J. A.

AU - Agarwal, P.

AU - Naraghirad, E.

PY - 2023/4/11

Y1 - 2023/4/11

N2 - This paper adopts the transcendental Bernstein series (TBS), a set of basis functions based on the Bernstein polynomials (BP), for approximating analytical functions. The TBS is more accurate than the BP method, particularly in approximating functions including one or more transcendental terms. The numerical results reveal also the applicability and higher computational efficiency of the new approach.

AB - This paper adopts the transcendental Bernstein series (TBS), a set of basis functions based on the Bernstein polynomials (BP), for approximating analytical functions. The TBS is more accurate than the BP method, particularly in approximating functions including one or more transcendental terms. The numerical results reveal also the applicability and higher computational efficiency of the new approach.

KW - Bernstein polynomials

KW - Transcendental Bernstein series

KW - Transcendental functions

UR - https://www.scopus.com/pages/publications/85204278814

M3 - Chapter

AN - SCOPUS:85204278814

SN - 9789815079340

SP - 73

EP - 93

BT - Advances in Special Functions of Fractional Calculus

PB - Bentham Science Publishers

ER -

Transcendental bernstein series: Interpolation and approximation

Abstract

Keywords

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