Quasilinear Interpolation by Minimal Splines

The paper studies quasilinear interpolation by minimal splines constructed on nonuniform grids with multiple nodes. Asymptotic representations for normalized splines are obtained. The sharpness of biorthogonal approximation and the order of accuracy of quasilinear interpolation with respect to the g...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 281; no. 2; pp. 285 - 296
Main Authors Livshits, L. P., Makarov, A. A., Makarova, S. V.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2024
Springer Nature B.V
Subjects
Approximation
Interpolation
Mathematical analysis
Mathematics
Mathematics and Statistics
Spline functions
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Summary:The paper studies quasilinear interpolation by minimal splines constructed on nonuniform grids with multiple nodes. Asymptotic representations for normalized splines are obtained. The sharpness of biorthogonal approximation and the order of accuracy of quasilinear interpolation with respect to the grid stepsize are established. Results of numerical experiments on approximating some test functions, which demonstrate the effect of choosing a generating vector function in constructing the corresponding minimal spline, are presented.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07101-4