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The Wavelet Digest
   -> Volume 2, Issue 15

Preprints available
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Author Message
Silvia Bertoluzza, IAN-CNR Pavia (Italy)

PostPosted: Fri Nov 29, 2002 3:37 pm    
Subject: Preprints available
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Preprints available

Preprint can be requested for the following papers:

"Some Remarks on Wavelet Interpolation"

by S. Bertoluzzza, G. Naldi

Abstract: In this paper we present some results regarding wavelet
interpolation. After discussing the characterization of interpolating
scaling functions we give two examples of construction of an interpolation
operator in the framework of a multiresolution analysis, the first obtained
by constructing an interpolating scaling function in a given multiresolution
analysis, and the second based on the autocorrelation function of a
compactly supported Daubechies wavelet. For both examples we give an
estimate on the order of the interpolation error.

"A wavelet Collocation Method for the Numerical Solution of PDE's"

We present a wavelet collocation method for the numerical solution
of partial differential equations. Such a method is based on the use of the
autocorrelation functions of I. Daubechies's compactly supported wavelets.
We study from the theoretical point of view
the application of such a method to the solution of an elliptic constant
coefficients partial differential equation on the line, proving stability and
an error estimate. Due to the particular
form of the trial functions we chose, we remark that we get the same
linear system which arises in the application of the wavelet Galerkin method
Daubechies wavelets. However, due to the higher regularity and to the better
approximation properties, the collocation method has higher order.
In the last section we will present results of such a method tested
on two simple elliptic boundary value problems on the interval.


Point of contact for preprint:
Silvia Bertoluzza,
v. Abbiategrasso 209
27100 Pavia (Italy)
E-mail: Sil26@IPVIAN.bitnet
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