Open AccessAsymptotics of $L_p$-error for adaptive approximation of $n$-variable functions by harmonic splines
Author(s) -
T.Yu. Leskevich
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241112
Subject(s) - differentiable function , mathematics , unit cube , harmonic , sequence (biology) , cube (algebra) , harmonic function , variable (mathematics) , mathematical analysis , spline (mechanical) , function (biology) , approximation error , combinatorics , physics , quantum mechanics , evolutionary biology , biology , genetics , thermodynamics
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.