EuDML | Browse

The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two...

Reference points based transformation and approximation

Csaba Török (2013)

Kybernetika

Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new $r$ -point transformation that yields a function with a simpler geometrical structure than the original function. It uses $r \geq 2$ reference points and decreases the polynomial degree by $r - 1$ . Then a general representation of polynomials is proposed based on $r \geq 1$ reference...

Relèvement polynômial de traces et applications

Christine Bernardi, Yvon Maday (1990)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Reliable Rational Interpolation.

T.R. Hopkins, P.R. Graves-Morris (1980/1981)

Numerische Mathematik

Ritz-Galerkin Approximations in Blending Function Spaces.

J.C. Cavendish, C.A. Hall, W.J. Gordon (1976)

Numerische Mathematik

Sard Kernel Theorems on Triangular Domains with Application to Finite Element Error Bounds.

R.E. Barnhill, J.A. Gregory (1975/1976)

Numerische Mathematik

Several notes on the circumradius condition

Václav Kučera (2016)

Applications of Mathematics

Recently, the so-called circumradius condition (or estimate) was derived, which is a new estimate of the $W^{1, p}$ -error of linear Lagrange interpolation on triangles in terms of their circumradius. The published proofs of the estimate are rather technical and do not allow clear, simple insight into the results. In this paper, we give a simple direct proof of the $p = \infty$ case. This allows us to make several observations such as on the optimality of the circumradius estimate. Furthermore, we show how the case...

Shape preserving rational cubic interpolation.

Muhammad Sarfraz (1993)

Extracta Mathematicae

Simultaneous L1 Approximation of a Compact Set of Real-Valued Functions.

M.P. Carroll (1972)

Numerische Mathematik

Smooth approximation of data with applications to interpolating and smoothing

Segeth, Karel (2013)

Programs and Algorithms of Numerical Mathematics

In the paper, we are concerned with some computational aspects of smooth approximation of data. This approach to approximation employs a (possibly infinite) linear combinations of smooth functions with coefficients obtained as the solution of a variational problem, where constraints represent the conditions of interpolating or smoothing. Some 1D numerical examples are presented.

Smooth approximation spaces based on a periodic system

Segeth, Karel (2015)

Programs and Algorithms of Numerical Mathematics

A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system $exp (- k x)$ ....