Asymptotics of $$$L_p$$$-error for adaptive approximation of $$$n$$$-variable functions by harmonic splines

T.Yu. Leskevich (Oles Honchar Dnipropetrovsk National University)

Abstract


For a twice continuously differentiable function, defined on $$$n$$$-dimensional unit cube, we obtain sharp asymptotics of $$$L_p$$$-error for approximation by harmonic splines, and construct the asymptotically optimal sequence of partitions.

Keywords


spline; harmonic function; approximation; error

References


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Babenko Yu., Leskevich T. "On the $$$L_p$$$-error of adaptive approximation of bivariate functions by harmonic splines", Applicable Analysis, 2011; 17(7): pp. 124-137.

Babenko Yu., Leskevich T., Mirebeau J.-M. "Sharp asymptotics of the $$$L_p$$$ approximation error for interpolation on block partitions", Numer. Math., 2011; 117(3): pp. 397-424. doi:10.1007/s00211-010-0355-y




DOI: https://doi.org/10.15421/241112

  

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Copyright (c) 2011 T.Yu. Leskevich

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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