Displaying similar documents to “Smooth approximation and its application to some 1D problems”

Smooth approximation of data with applications to interpolating and smoothing

Segeth, Karel

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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.

Onesided approximation and real interpolation.

N. Krugljak, E. Matvejev (1997)

Collectanea Mathematica

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It is proved that the reiteration theorem is not valid for the spaces Ap (theta,q) defined by V. Popov by means of onesided approximation. It is also proved that a class of cones, defined by onesided approximation of piecewise linear functions on the interval [0,1], is stable for the real interpolation method.

Some remarks on mixed approximation problem

Sýkorová, Irena

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Several years ago, we discussed the problem of approximation polynomials with Milan Práger. This paper is a natural continuation of the work we collaborated on. An important part of numerical analysis is the problem of finding an approximation of a given function. This problem can be solved in many ways. The aim of this paper is to show how interpolation can be combined with the Chebyshev approximation.

Smooth approximation spaces based on a periodic system

Segeth, Karel

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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...