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 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.

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 .

scholarly journals Lebesgue Constant Using Sinc Points

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Maha Youssef ◽  
Hany A. El-Sharkawy ◽  
Gerd Baumann
Keyword(s):  
Upper Bound ◽  
Lebesgue Constant ◽  
Upper Bounds ◽  
Chebyshev Points ◽  
Set Of Points ◽  
Barycentric Form

Lebesgue constant for Lagrange approximation at Sinc points will be examined. We introduce a new barycentric form for Lagrange approximation at Sinc points. Using Thiele’s algorithm we show that the Lebesgue constant grows logarithmically as the number of interpolation Sinc points increases. A comparison between the obtained upper bound of Lebesgue constant using Sinc points and other upper bounds for different set of points, like equidistant and Chebyshev points, is introduced.

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
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