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2019 | OriginalPaper | Buchkapitel

Properties of One Method for the Spline Approximation

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Abstract

In the article the influence of the basic functions used to represent a polynomial from the current spline link on the approximating properties of the semi-local smoothing spline, proposed by D.A. Silaev, is studied. When constructing splines of this type, a recurrence formula that binds the group of coefficients of a polynomial from a previous spline link with a similar group of polynomial coefficients from the current spline link, is used. Silayev D.A. were studied the properties of the spline using only a power basis.
It is shown that the study of the magnitude of the eigenvalues of the matrix of stability, which is used in the algorithm for constructing the investigated spline, is not enough to predict the approximation properties of this spline. The accuracy of the approximation is also significantly influenced by the number of conditionality of the matrix, which is a block from the traditional matrix of the least squares method. It is shown that the transition to polynomials, which are presented in the form of certain Hermite polynomials, is expedient. When using semi-local splines, the number of spline units decreases in comparison with the interpolation spline on the same grid. But a significant reduction in the description of the spline does not lead to a marked deterioration in the accuracy of the solutions of boundary value problems solved with the help of splines of the investigated species. The obtained theoretical results are confirmed at solving practical problems.

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Literatur
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Metadaten
Titel
Properties of One Method for the Spline Approximation
verfasst von
I. O. Astionenko
P. I. Guchek
A. N. Khomchenko
O. I. Litvinenko
G. Ya. Tuluchenko
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-319-99996-8_5