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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Richtmyer R.D. Principles of Advanced Mathematical Physics, Mir, 1982. (in Russian) doi:10.1007/978-3-642-46378-5

Babenko V., Babenko Yu., Skorokhodov D. "Exact asymptotics of the optimal $$$L_p$$$-error of linear spline interpolation", East J. Approx, 2008; 14(3): pp. 285-317.

Babenko V., Babenko Yu., Ligun A., Shumeiko A. "On asymptotical behaviour of the optimal linear spline interpolation error of $$$C^2$$$ functions", East J. Approx, 2006; 12(1): pp. 71-101.

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


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