On the $L_p$-error of approximation of bivariate functions by harmonic splines
arXiv:1101.26964 citationsh-index: 6
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Provides theoretical error bounds for harmonic splines, but the contribution is incremental for researchers in approximation theory.
The paper analyzes harmonic spline interpolation as an alternative to polynomial spline interpolation for bivariate functions, presenting asymptotic $L_p$-error results for adaptive approximation.
Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the $L_p$-error for adaptive approximation by harmonic splines.