Optimal asymptotic Lebesgue constant of Berrut’s rational interpolation operator for equidistant nodes

2017 ◽  
Vol 294 ◽  
pp. 139-145
Author(s):  
Ren-Jiang Zhang
Keyword(s):  
Lebesgue Constant ◽  
Rational Interpolation ◽  
Interpolation Operator ◽  
Equidistant Nodes

scholarly journals On the Lebesgue constant of barycentric rational interpolation at equidistant nodes

2011 ◽  
Vol 121 (3) ◽  
pp. 461-471 ◽  
Author(s):  
Len Bos ◽  
Stefano De Marchi ◽  
Kai Hormann ◽  
Georges Klein
Keyword(s):  
Lebesgue Constant ◽  
Rational Interpolation ◽  
Equidistant Nodes ◽  
Barycentric Rational Interpolation

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

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
Sign in / Sign up

Export Citation Format

Share Document