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   -> Volume 4, Issue 6

Software: Computing Refinable Integrals
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Angela Kunoth (

PostPosted: Tue Dec 03, 2002 1:19 pm    
Subject: Software: Computing Refinable Integrals
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Software: Computing Refinable Integrals

Author: Angela Kunoth

Applications: * Evaluating refinable functions in 1D-3D
* Computing inner products in 1D-3D
* Computing entries of stiffness matrices
in Petrov-Galerkin schemes in 1D-3D

Based on the theory developed in [W.Dahmen, C.A. Micchelli, Using
the refinement equation for evaluating integrals of wavelets, Siam
J. Numer. Anal. 30, 1993, 507-537], I have written a C++-program
that computes function values and derivatives of refinable functions
(generators) and integrals of refinable functions for up to four
factors in the integral in one and two dimensions. In three dimensions,
integrals with at most three factors can be computed. The routines
calculate the desired values exactly up to round-off while avoiding
any quadrature rules by using the refinement equations for the
computations. As input data, only the mask coefficients of the
refinable functions and some parameters like the dimension of the
underlying domain and the number of refinable functions are needed.

A comprehensive documentation of the program in latex-format called

Computing Refinable Integrals --- Documentation of the Program
--- Version 1.1 ---

which summarizes the theory and contains several examples (Daubechies'
generators, B- and Box Splines) can be obtained via anonymous ftp as

> ftp
login: anonymous
password: your e-mail address
>cd reports
>get (or alternatively, inn.dvi.Z, inn.dvi.gz)

then uncompress (or unzip) file. The documentation contains
directions how to obtain the program.

In a future version, I intend to include a special treatment of the
tensor product case. Also I hope to modify the program soon such that
four factors in 3D-integrals can be computed.
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