Talks given at NuHAG events

Harmonic Polysplines

  W. R. Madych

  given at  strobl07 (20.06.07 10:00)
  id:  649
  length:  25min
  status:  accepted
  type:  talk
Polysplines, christened and promoted by
Ognyan Kounchev [1], are natural multivariate
analogues of classical univariate piecewise polynomial
In this work we establish properties of
harmonic polysplines that interpolate
arbitrary distributions defined on parallel
In particular we show the following:
(a) Such polysplines provide a
solution to the natural minimization problem
involving the class of distributions whose
gradient is square integrable. (b)
In the case when the data are polynomials
such polysplines coincide with harmonic
polynomials on the slabs which are determined
by the parallel hyperplanes. \\

[1] O. Kounchev,
{\em Multivariate Polysplines: Applications to Numerical
and Wavelet Analysis}, Academic Press,
San Diego, 2001.

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