scholarly journals Lebesgue constant for the Strömberg wavelet

2003 ◽  
Vol 122 (1) ◽  
pp. 13-23
Author(s):  
Paweł Bechler
Keyword(s):  
Lebesgue Constant

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 tighter upper bound on the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

2016 ◽  
Vol 59 ◽  
pp. 71-78 ◽  
Author(s):  
Chongyang Deng ◽  
Shankui Zhang ◽  
Yajuan Li ◽  
Wenbiao Jin ◽  
Yi Zhao
Keyword(s):  
Upper Bound ◽  
Lebesgue Constant ◽  
Equidistant Nodes

scholarly journals The Lebesgue function for generalized Hermite-Fejér interpolation on the Chebyshev nodes

2000 ◽  
Vol 42 (1) ◽  
pp. 98-109 ◽  
Author(s):  
Graeme J. Byrne ◽  
T. M. Mills ◽  
Simon J. Smith
Keyword(s):  
Asymptotic Expansion ◽  
Chebyshev Polynomial ◽  
Lebesgue Constant ◽  
Local Maximum ◽  
Lebesgue Function ◽  
Chebyshev Nodes ◽  
Short Survey ◽  
Convergence Results ◽  
Limiting Behaviour

AbstractThis paper presents a short survey of convergence results and properties of the Lebesgue function λm,n(x) for(0, 1, …, m)Hermite-Fejér interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n → ∞ of the Lebesgue constant Λm,n = max{λm,n(x): −1 ≤ x ≤ 1} for even m is then studied, and new results are obtained for the asymptotic expansion of Λm,n. Finally, graphical evidence is provided of an interesting and unexpected pattern in the distribution of the local maximum values of λm,n(x) if m ≥ 2 is even.

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