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Regularizing properties of explicit approximating splines

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Abstract

A method is proposed for the solution of some operator equations of the first kind by successive smoothing of the righthand side using an explicit spline approximation and by numerical inversion of the operator. For the relevant class of problems, the regularizing properties of the method are reduced on the whole to the regularizing properties of explicit spline approximation, which are studied under certain assumptions about errors in input data and the discretization step.

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Additional information

Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 39–46, 1986.

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Grebennikov, A.I. Regularizing properties of explicit approximating splines. Comput Math Model 1, 132–136 (1990). https://doi.org/10.1007/BF01129054

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Keywords

  • Mathematical Modeling
  • Input Data
  • Computational Mathematic
  • Industrial Mathematic
  • Operator Equation