caa a22 4500 378939955 CHVBK 20180305123649.0 cr unu---uuuuu 161128e20041001xx s 000 0 eng 10.1515/1569398042395961 doi (NATIONALLICENCE)gruyter-10.1515/1569398042395961 Smelov V. V. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of theRussian Academy of Sciences, Novosibirsk 630090, Russia Effective approximation of piecewise smooth functions by their expansion into fast convergent series in terms of functions formed by eigenfunctions of Sturm-Liouvilleproblems [Elektronische Daten] [V. V. Smelov] Using the eigenfunctions of two Sturm-Liouville problems (with the same operator of a general form but with two different versions of boundary conditions), a method for constructing these specific basis functions is developed. The corresponding expansions of smooth and piecewise smooth functions in terms of such basis lead to fast convergent series. This result makes it possible to approximate the functions of the above class by a small number of terms. We also give brief information on a method for constructing multidimensional (in particular, two-dimensional) specific basis functions with the above properties. The proposed method is based on the ideas of the author's earlier works. However, it is, in essence, a new method that has substantially improved characteristics and is mainly oriented to the approximation of piecewise smooth functions. We also consider several important special cases. Copyright 2004, Walter de Gruyter Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 19/5(2004-10-01), 449-465 0927-6467 19:5<449 2004 19 rnam https://doi.org/10.1515/1569398042395961 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569398042395961 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Smelov V. V. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of theRussian Academy of Sciences, Novosibirsk 630090, Russia NATIONALLICENCE 773 0- Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 19/5(2004-10-01), 449-465 0927-6467 19:5<449 2004 19 rnam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter