Uniform convergence of lagrange interpolation processes

1986 ◽  
Vol 39 (2) ◽  
pp. 124-133
Author(s):  
A. A. Privalov
Keyword(s):  
Uniform Convergence ◽  
Lagrange Interpolation

Uniform convergence of derivatives of extended Lagrange interpolation

1991 ◽  
Vol 60 (1) ◽  
pp. 195-218 ◽  
Author(s):  
Giuliana Criscuolo ◽  
Giuseppe Mastroianni ◽  
Donatella Occorsio
Keyword(s):  
Uniform Convergence ◽  
Lagrange Interpolation ◽  
Derivatives Of

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 Bivariate uniform approximation via bivariate Lagrange interpolation polynomials

2014 ◽  
Vol 23 (1) ◽  
pp. 7-13
Author(s):  
DAN BARBOSU ◽  
◽  
OVIDIU T. POP ◽  
Keyword(s):  
Uniform Convergence ◽  
Uniform Approximation ◽  
Lagrange Interpolation ◽  
Sufficient Conditions ◽  
Interpolation Formula ◽  
Interpolation Theory ◽  
Science Publisher ◽  
Lagrange Interpolation Formula ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials

In the present note, we extend some univariate uniform approximation results by means of Lagrange interpolating polynomials [Ivan, M., Elements of Interpolation Theory, Mediamira Science Publisher, Cluj-Napoca (2004)] to the bivariate case. It is well known that generally, in the univariate case, the sequence of Lagrange interpolation polynomials does’t converges to the approximated function. This fact was first observed by G. Faber (see [9]), which constructed an example when the sequence of Lagrange interpolation polynomials diverges. The result of G. Faber was more generalized by I. Muntean (see [12]). M. Ivan established first sufficient conditions for the uniform convergence of the sequence of Lagrange interpolation polynomials associated to a univariate real valued function. First, we represent the remainder term of bivariate Lagrange interpolation formula in terms of bivariate divided difference. Using this representation we establish sufficient conditions for the uniform convergence of the sequence of bivariate Lagrange interpolation polynomials to the approximated function.

QUASI-UNIFORM CONVERGENCE AND ℒ-SPACES

1992 ◽  
Vol 18 (2) ◽  
pp. 321 ◽  
Author(s):  
Bukovská ◽  
Bukovský ◽  
Ewert
Keyword(s):  
Uniform Convergence

Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces
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