scholarly journals The order of Lebesgue constant of Lagrange interpolation on several intervals

2016 ◽  
Vol 72 (2) ◽  
pp. 103-111 ◽  
Author(s):  
A. L. Lukashov ◽  
J. Szabados
Keyword(s):  
Lagrange Interpolation ◽  
Lebesgue Constant ◽  
Several Intervals

scholarly journals Multivariate Lagrange Interpolation at Sinc Points Error Estimation and Lebesgue Constant

2016 ◽  
Vol 8 (4) ◽  
pp. 118 ◽  
Author(s):  
Maha Youssef ◽  
Hany A. El-Sharkawy ◽  
Gerd Baumann
Keyword(s):  
Uniform Convergence ◽  
Error Estimation ◽  
Upper Bound ◽  
Lagrange Interpolation ◽  
Lebesgue Constant ◽  
Explicit Construction ◽  
Interpolation Operator ◽  
Lebesgue Constants ◽  
Set Of Points

This paper gives an explicit construction of multivariate Lagrange interpolation at Sinc points. A nested operator formula for Lagrange interpolation over an $m$-dimensional region is introduced. For the nested Lagrange interpolation, a proof of the upper bound of the error is given showing that the error has an exponentially decaying behavior. For the uniform convergence the growth of the associated norms of the interpolation operator, i.e., the Lebesgue constant has to be taken into consideration. It turns out that this growth is of logarithmic nature $O((log n)^m)$. We compare the obtained Lebesgue constant bound with other well known bounds for Lebesgue constants using different set of points.

scholarly journals A link between Lebesgue constants and Hermite-Fejér interpolation

1986 ◽  
Vol 33 (2) ◽  
pp. 207-218 ◽  
Author(s):  
S. J. Goodenough
Keyword(s):  
Rate Of Convergence ◽  
Lagrange Interpolation ◽  
Historical Perspective ◽  
Lebesgue Constant ◽  
The Other ◽  
Lebesgue Constants ◽  
Close Link ◽  
The One ◽  
Image Position ◽  
Interpolation Polynomials

A review of the development of estimates for Lebesgue constants associated with Lagrange interpolation on the one hand, and estimates for the rate of convergence of Hermite-Fejér interpolation on the other hand, provides a historical perspective for the following surprising, close link between these apparently diverse concepts. Denoting by Λn (T) the Lebesgue constant of order n and by Δn (T) the maximum interpolation error for functions of class Lip 1 by Hexmite-Fejér interpolation polynomials of degree not exceeding 2n − 1, based on the zeros of the Chebyshev polynomial of first kind, we discover that, for even values of n, Λn(T) = n Δn(T).

Lebesgue constant for Lagrange interpolation on equidistant nodes

2004 ◽  
Vol 20 (4) ◽  
pp. 323-331 ◽  
Author(s):  
A. Eisinberg ◽  
G. Fedele ◽  
G. Franzè
Keyword(s):  
Lagrange Interpolation ◽  
Lebesgue Constant ◽  
Equidistant Nodes

scholarly journals Upper Bound for Lebesgue Constant of Bivariate Lagrange Interpolation Polynomial on the Second Kind Chebyshev Points

2022 ◽  
Vol 2022 ◽  
pp. 1-19
Author(s):  
Juan Liu ◽  
Laiyi Zhu
Keyword(s):  
Upper Bound ◽  
Chebyshev Polynomials ◽  
Lagrange Interpolation ◽  
Lebesgue Constant ◽  
Interpolation Polynomial ◽  
Growth Order ◽  
Lagrange Interpolation Polynomial ◽  
Chebyshev Points ◽  
The Common ◽  
Common Zeros

In the paper, we study the upper bound estimation of the Lebesgue constant of the bivariate Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the second kind on the square − 1,1 2 . And, we prove that the growth order of the Lebesgue constant is O n + 2 2 . This result is different from the Lebesgue constant of Lagrange interpolation polynomial on the unit disk, the growth order of which is O n . And, it is different from the Lebesgue constant of the Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the first kind on the square − 1,1 2 , the growth order of which is O ln n 2 .

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