Copyright since 2001, Bin Han, University of Alberta,
All Rights Reserved
The use of all the following software is permitted for
non-commercial, educational, and research use only. The software
and/or related materials are provided "as-is" without warranty of any
kind including any warranties of performance or merchantability or
fitness for a particular use or purpose or for any purpose
whatsoever, for the licensed product, however used. In no event shall
University of Alberta and/or Bin Han be liable for any damages and/or
costs, including but not limited to incidental or consequential
damages of any kind, including economic damage or injury to property
and lost profits, regardless of whether University of Alberta shall
be advised, have reason to know, or in fact shall know of the
possibility. User bears all risk relating to quality and performance
of the software and/or related materials.
Any use other than non-commercial, educational, or research, or any
redistribution in original or modified form requires prior written
authorization from the copyright holder.
Report errors, mistakes, and bugs to Bin Han at bhan@ualberta.ca.
Send comments/suggestions to Bin Han at bhan@ualberta.ca
==========================================================
MAPLE 6.0 routines for CBC algorithms on constructing 1D/2D
biorthogonal multiwavelets or Hermite Interpolatory masks with
a general dilation factor (1D) or a dilation matrix
This set of Maple routines contains the following 7 files
copyright
README
basicall
d1cbc
d2cbc
example1
example2
Explanation:
basicall---some basic MAPLE routines.
d1cbc---MAPLE routines to handle 1D multiwavelets,
Hermite interpolatory mask, biorthogonal
multiwavelets by CBC algorithm etc., with a
general dilation factor
d2cbc---MAPLE routines to handle 2D multiwavelets,
Hermite interpolatory mask, biorthogonal
multiwavelets by CBC algorithm etc., with
a general 2 by 2 dilation matrix.
example1 ---how to obtain 1D Hermite interpolatory
masks and dual masks using CBC algorithm
example2 ---how to obtain 2D Hermite interpolatory
masks and dual masks using CBC algorithm
Check the indivisual file for more explanation of the
MAPLE routines.
=============================================
Some directly related references:
For symmetry of a refinable function and mask with a dilation matrix
see the papers
Bin Han, Symmetry property and construction of wavelets with a
general dilation matrix, Linear Algebra and Its Applications,
(2001), to appear.
Bin Han, Computing the smoothness exponent of a symmetric
multivariate refinable function, (2001), preprint
Bin Han, Thomas P.-Y. Yu, Bruce Piper,
Multivariate Refinable Hermite Interpolants, (2002), preprint.
For CBC algorithms on constructing biorthogonal multiwavelets.
CBC stands for Coset By Coset
These program is mainly based on the following paper
Bin Han, Hermite interpolants and biorthogonal multiwavelets
with arbitrary order of vanishing moments (1999) SPIE
Proc. Vol. 3813, pp. 147--161.
The CBC algorithm for the multivariate multiwavelets with
a general dilation matrix was established.
Also, see the following papers for the CBC algorithm
Bin Han, Analysis and Construction of Optimal Multivariate
Biorthogonal Wavelets With Compact Support, SIAM Journal on
Mathematical Analysis, Vol. 31, No.2 (1999/2000), 274--304.
CBC algorithm for interpolatory masks with dilation
matrix 2I_s was first introduced in this paper.
Di-Rong Chen, Bin Han and Sherman D. Riemenschneider,
Construction of Multivariate Biorthogonal Wavelets With
Arbitrary Vanishing Moments, Advances in Computational
Mathematics, Vol. 13 No. 2 (2000), 131-165.
CBC alogrithm for the scalar case with a general dilation
matrix was established.
Bin Han and Rong-Qing Jia, Quincunx Fundamental Refinable
Functions and Quincunx Biorthogonal Wavelets, Mathematics of
Computation, Vol. 71, No. 237, (2002), 165--196.
CBC algorithm for quincunx wavelets was discussed
Bin Han, Construction of multivariate biorthogonal wavelets by
CBC algorithm. Wavelet analysis and multiresolution methods
(Urbana-Champaign, IL, 1999), 105--143, Lecture Notes in Pure
and Appl. Math., 212, Dekker, New York, 2000.
Survey paper on CBC algorithm.
Bin Han, Hermite interpolants and biorthogonal multiwavelets
with arbitrary order of vanishing moments (1999) SPIE
Proc. Vol. 3813, pp. 147--161.
Survey paper on CBC algorithm for 1-dimensional multiwavelets.
Papers can be downloaded at
http://www.ualberta.ca/~bhan/publ.htm
Program was developed by Bin Han at University of Alberta
Version 1 on January 6, 2002.
Initial Tests of the program have been done on January 6, 2002.
Report bugs, mistakes, errors, comments, suggestions etc. to
Bin Han, bhan@ualberta.ca, htpp://www.ualbert.ca/~bhan