Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial

The generalized polynomials such as Chebyshev polynomial and Hermite polynomial are widely used in interpolations and numerical fittings and so on. Therefore, it is significant to study inclusion regions of the zeros for generalized polynomials. In this paper, several new inclusion sets of zeros for...

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Main Authors:	Xiao Feng, Yaotang Li
Format:	Article
Language:	English
Published:	MDPI AG 2019-02-01
Series:	Mathematics
Subjects:	the inclusion region of polynomial zeros Chebyshev polynomials Brauer theorem oval of Cassini comrade matrix
Online Access:	https://www.mdpi.com/2227-7390/7/2/155

id	doaj-5e54d957c2314f84a752406f7c4560aa
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spelling	doaj-5e54d957c2314f84a752406f7c4560aa2020-11-24T21:16:12ZengMDPI AGMathematics2227-73902019-02-017215510.3390/math7020155math7020155Brauer-Type Inclusion Sets of Zeros for Chebyshev PolynomialXiao Feng0Yaotang Li1School of Mathematics and Statistics, Yunnan University, Kunming 650091, ChinaSchool of Mathematics and Statistics, Yunnan University, Kunming 650091, ChinaThe generalized polynomials such as Chebyshev polynomial and Hermite polynomial are widely used in interpolations and numerical fittings and so on. Therefore, it is significant to study inclusion regions of the zeros for generalized polynomials. In this paper, several new inclusion sets of zeros for Chebyshev polynomials are presented by applying Brauer theorem about the eigenvalues of the comrade matrix of Chebyshev polynomial and applying the properties of ovals of Cassini. Some examples are given to show that the new inclusion sets are tighter than those provided by Melman (2014) in some cases.https://www.mdpi.com/2227-7390/7/2/155the inclusion region of polynomial zerosChebyshev polynomialsBrauer theoremoval of Cassinicomrade matrix
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xiao Feng Yaotang Li
spellingShingle	Xiao Feng Yaotang Li Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial Mathematics the inclusion region of polynomial zeros Chebyshev polynomials Brauer theorem oval of Cassini comrade matrix
author_facet	Xiao Feng Yaotang Li
author_sort	Xiao Feng
title	Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial
title_short	Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial
title_full	Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial
title_fullStr	Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial
title_full_unstemmed	Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial
title_sort	brauer-type inclusion sets of zeros for chebyshev polynomial
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-02-01
description	The generalized polynomials such as Chebyshev polynomial and Hermite polynomial are widely used in interpolations and numerical fittings and so on. Therefore, it is significant to study inclusion regions of the zeros for generalized polynomials. In this paper, several new inclusion sets of zeros for Chebyshev polynomials are presented by applying Brauer theorem about the eigenvalues of the comrade matrix of Chebyshev polynomial and applying the properties of ovals of Cassini. Some examples are given to show that the new inclusion sets are tighter than those provided by Melman (2014) in some cases.
topic	the inclusion region of polynomial zeros Chebyshev polynomials Brauer theorem oval of Cassini comrade matrix
url	https://www.mdpi.com/2227-7390/7/2/155
work_keys_str_mv	AT xiaofeng brauertypeinclusionsetsofzerosforchebyshevpolynomial AT yaotangli brauertypeinclusionsetsofzerosforchebyshevpolynomial
_version_	1726016598794305536

Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial

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