Interpolation Polynomials Which Give Best Order of Approximation Among Continuously Differentiable Functions of Arbitrary Fixed Order on [ -1, + 1 ]

1974 ◽  
Vol 200 ◽  
pp. 419
Author(s):  
A. K. Varma
Keyword(s):  
Order Of Approximation ◽  
Differentiable Functions ◽  
Fixed Order ◽  
Interpolation Polynomials

scholarly journals On the continuity of multivariate Lagrange interpolation at natural lattices

2013 ◽  
Vol 16 ◽  
pp. 45-60 ◽  
Author(s):  
J.-P. Calvi ◽  
V. M. Phung
Keyword(s):  
Lagrange Interpolation ◽  
Geometric Condition ◽  
Taylor Polynomial ◽  
Fixed Degree ◽  
Differentiable Functions ◽  
Interpolation Polynomials

AbstractWe give a natural geometric condition that ensures that sequences of interpolation polynomials (of fixed degree) of sufficiently differentiable functions with respect to the natural lattices introduced by Chung and Yao converge to a Taylor polynomial.

scholarly journals Lower estimates on the saturation order of approximation of twice continuously differentiable functions by piecewise constants on convex partitions

2018 ◽  
Vol 26 (1) ◽  
pp. 37 ◽  
Author(s):  
O.V. Kozynenko
Keyword(s):  
Approximation Order ◽  
Order Of Approximation ◽  
Piecewise Constant ◽  
Differentiable Functions ◽  
Convex Partitions ◽  
Saturation Order ◽  
Piecewise Constant Approximation

We consider the problem of approximation order of twice continuously differentiable functions of many variables by piecewise constants. We show that the saturation order of piecewise constant approximation in $$$L_p$$$ norm on convex partitions with $$$N$$$ cells is $$$N^{-2/(d+1)}$$$, where $$$d$$$ is the number of variables.

scholarly journals On a Class of Hermite Interpolation Polynomials for Nonlinear Second Order Partial Differential Operators

2018 ◽  
Vol 173 ◽  
pp. 03023
Author(s):  
Leonid A. Yanovich ◽  
Marina V. Ignatenko
Keyword(s):  
Hermite Interpolation ◽  
Differential Operators ◽  
Second Order ◽  
Chebyshev System ◽  
Partial Differential ◽  
Differentiable Functions ◽  
Partial Differential Operators ◽  
Operator Interpolation ◽  
Interpolation Polynomials ◽  
Hermite Interpolation Polynomials

This article is devoted to the problem of construction of Hermite interpolation formulas with knots of the second multiplicity for second order partial differential operators given in the space of continuously differentiable functions of two variables. The obtained formulas contain the Gateaux differentials of a given operator. The construction of operator interpolation formulas is based on interpolation polynomials for scalar functions with respect to an arbitrary Chebyshev system of functions. An explicit representation of the interpolation error has been obtained.

Matching of resummation with fixed order NNLO for event shapes

2008 ◽  
Author(s):  
Gionata Luisoni ◽  
Thomas Gehrmann ◽  
Hasko Stenzel
Keyword(s):  
Fixed Order ◽  
Event Shapes
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