An Adaptive Local Procedure to Approximate Unevenly Distributed Data

Mira Bozzini, Licia Lenarduzzi

Abstract


We propose an adaptive local procedure, which uses the modified Shepard’s method
with local polyharmonic interpolants. The aim is to reconstruct, in a faithful way, a
function known by a large and highly irregularly distributed sample. Such a problem is
generally related to the recovering of geophysical surfaces, where the sample is measured
according to the behaviour of the surface.
The adaptive local procedure is used to calculate, by an efficient algorithm, an interpolating
polyharmonic function, when a very large sample is assigned.
When we consider a sample of size N < 104, we propose an approximating polyharmonic
function obtained by combining adaptively a global interpolant, relevant to a
subset of the data, with local adaptive interpolants.
The goodness of the approximating functions in two different cases is shown by real
examples.

[DOI: 10.1685/CSC09260] About DOI

Keywords


Polyharmonic functions, Shepard's method, interpolation, adaptivity, unevenly distributed data.

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DOI: http://dx.doi.org/10.1685/




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