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.

Data approximation using polyharmonic radial basis functions

Segeth, Karel

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The paper is concerned with the approximation and interpolation employing polyharmonic splines in multivariate problems. The properties of approximants and interpolants based on these radial basis functions are shown. The methods of such data fitting are applied in practice to treat the problems of, e.g., geographic information systems, signal processing, etc. A simple 1D computational example is presented.