A Note on Lagrange Interpolation of | x | on the Chebyshev and Chebyshev-Lobatto Nodal Systems: The Even Cases

被引：0

作者：

Berriochoa, Elias ^{[1
]}

Cachafeiro, Alicia ^{[1
]}

Garcia-Rabade, Hector ^{[2
]}

Manuel Garcia-Amor, Jose ^{[3
]}

机构：

[1] Univ Vigo, Dept Matemat Aplicada 1, Vigo 36310, Spain

[2] Univ Vigo, Dept Matemat Aplicada 2, Orense 32004, Spain

[3] Inst ES Valle Inclan, Xunta Galicia, Pontevedra 36001, Spain

来源：

MATHEMATICS | 2022年 / 10卷 / 15期

关键词：

Lagrange interpolation; Chebyshev nodal systems; Chebyshev-Lobatto nodal systems; absolute value approximation; rate of convergence; Gibbs-Wilbraham phenomena; GIBBS PHENOMENON;

D O I：

10.3390/math10152558

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Throughout this study, we continue the analysis of a recently found out Gibbs-Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the error of the Lagrange polynomial interpolants of the function vertical bar x vertical bar on [-1, 1], using Chebyshev and Chebyshev-Lobatto nodal systems with an even number of points. Moreover, with respect to the odd cases, relevant changes in the shape and the extrema of the error are given.

引用

页数：14

共 40 条

[1] The Gibbs-Wilbraham phenomenon in the approximation of |x| by using Lagrange interpolation on the Chebyshev-Lobatto nodal systems
Berriochoa, E.
Cachafeiro, A.
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Rabade, H. Garcia
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 414
[2] A note on the rate of convergence for Chebyshev-Lobatto and Radau systems
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[3] A Minimal Chebyshev-Lobatto Formula of Degree 5 for the Square
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[4] The first kind Chebyshev-Lobatto quadrature rule and its numerical improvement
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Eslahchi, MR
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[5] BIVARIATE LAGRANGE INTERPOLATION AT THE CHEBYSHEV NODES
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[6] Lagrange interpolation with respect to Chebyshev systems and higher bruhat orders
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[7] Lagrange interpolation with respect to Chebyshev systems and higher Bruhat orders
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[8] Lagrange interpolation on Chebyshev points of two variables
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[9] Lagrange-Chebyshev Interpolation for image resizing
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MATHEMATICS AND COMPUTERS IN SIMULATION, 2022, 197 : 105 - 126
[10] Algorithms and convergence for Hermite interpolation based on extended Chebyshev nodal systems
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Illan, J.
APPLIED MATHEMATICS AND COMPUTATION, 2014, 234 : 223 - 236

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