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Wavelet Digest, Vol. 2, Nr. 14.
Wavelet Digest Tuesday, October 5, 1993 Volume 2 : Issue 14
Today's Editor: Wim Sweldens
sweldens@math.scarolina.edu
Today's Topics:
1. Electronic Journal of Differential Equations (EJDE)
2. Mathematica wavelet packets programs.
3. Wavelet Papers and MATLAB Software from Rice University.
4. Windows 3.1 implementation of the wavelet fingerprint compression.
5. Questions
6. Preprint available: Wavelet Function, Scaling function and DWT
7. Question: Wavelets on closed surfaces in 3D Euclidean Space?
8. ACHA: A new wavelet journal, first issue.
9. Question: Calculating the coefficients for the Chui wavelets?
10. CFP: "Time-frequency, Wavelets and Multiresolution", Lyon, France
11. Preprints available
Submissions for Wavelet Digest:
E-mail to wavelet@math.scarolina.edu with "submit" as subject.
Subscriptions for Wavelet Digest:
E-mail to wavelet@math.scarolina.edu with "subscribe" as subject.
To unsubscribe, e-mail with "unsubscribe" followed by your e-mail
address as subject. To change address, unsubscribe and resubscribe.
Archive site, preprints, references and back issues:
Anonymous ftp to maxwell.math.scarolina.edu (129.252.12.3),
directories /pub/wavelet and /pub/imi_93.
Gopher and Xmosaic server: bigcheese.math.scarolina.edu.
Current number of subscribers: 2887
--------------------------- Topic #1 -----------------------------------
From: Julio G. Dix, Southwest Texas State University.
Subject: Electronic Journal of Differential Equations (EJDE)
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (EJDE)
Mathematicians at Southwest Texas State University and
at the University of North Texas have collaborated to
establish a new journal, the ELECTRONIC JOURNAL OF
DIFFERENTIAL EQUATIONS (EJDE). The EJDE will be a strictly
electronic journal dealing with all aspects of differential
equations. Articles will be submitted as TeX files, sent to
referees electronically, and then disseminated electronically,
free of charge.
Although the time between submission and dissemination
will be greatly reduced, only original research of high
quality will be accepted. Each article will be subject to as
rigid a peer review process as is applied by the finest of
today's printed journals. The EJDE is calling for papers
now. There are no page charges.
The EJDE can be accessed via ftp (login: ftp), gopher, and
telnet (login: ejde) to "ejde.math.swt.edu" or to
"ejde.math.unt.edu". Examples illustrating these options are:
1. "telnet ejde.math.swt.edu", login: "ejde" . (It may be
necessary to set your terminal to emulate a VT100.)
2. "telnet e-math.ams.com", login: "e-math", password: "e-math",
select "Mathematical Publications", then "Other Mathematical
Publications", and then "Electronic Journal of Differential
Equations".
3. "ftp ejde.math.swt.edu", login: "ftp", and "cd pub".
4. Provided that the gopher-client software is loaded on the
reader's computer."gopher ejde.math.unt.edu".
Readers can transfer the TeX and Postscript files to
their own computers and then read them or print hard copies.
A free subscription to the abstracts of new articles in
the EJDE is available by sending an e-mail message to
"subs@ejde.math.swt.edu". Suggestions and comments should be sent
to "editor@ejde.math.unt.edu" or to "editor@ejde.math.swt.edu".
Identical copies of the EJDE will be originated and
maintained at Southwest Texas State University and at the
University of North Texas. For posterity and for interlibrary
loan, a hard copy exists in the libraries at both institutions.
The Managing Editors of EJDE are Alfonso Castro, Julio
Dix, Gregory Passty, and Ricardo Torrejon.
The Editorial Board consists of
P. Bates (Brigham Young University), A. Bloch (Ohio State University),
J. Bona (Pennsylvania State University), K. J. Brown (Heriot-Watt University),
L. Caffarelli (Institute for Advanced Study), C. Castillo-Chavez (Cornell),
C. Chui (Texas A & M University), M. Crandall (University of California at
Santa Barbara), E. Di Benedetto (Northwestern University), G. B. Ermentrout
(University of Pittsburgh), J. Escobar (Indiana University), L. C. Evans
(University of California at Berkeley), J. Goldstein (Louisiana State
University), C. Groetsch (University of Cincinnati), I. Herbst (University
of Virginia), C. Kenig (University of Chicago), R. Kohn (Courant Institute),
A. Lazer (Miami University), J. Neuberger (University of North Texas),
P. H. Rabinowitz (University of Wisconsin), R. Shivaji (Mississippi State
University), R. Showalter (University of Texas), H. Smith (Arizona State
University), P. Souganidis (University of Wisconsin), N. Walkington
(Carnegie-Mellon University),
--------------------------- Topic #2 -----------------------------------
From: Mladen Victor Wickerhauser, Washington University.
Subject: Mathematica wavelet packets programs.
Here are some old Mathematica programs to generate individual wavelet packets
and to calculate inner products with individual wavelet packets. The one
example I have provided is intended to be a template: change the relevant
parameters, or the sequence of filters, to get any wavelet packet you wish.
I hereby put this code into the public domain.
Cheers, Victor
Professor Mladen Victor Wickerhauser <victor@math.wustl.edu>
Department of Mathematics, Campus Box 1146, One Brookings Drive,
Washington University in Saint Louis, Missouri 63130 USA
Telephone: USA+(314)935-6771; Facsimile: USA+(314)935-5799
(* ----------------->8 Cut here 8<---------------------*)
(* Wave Packets and Modulated Pulses *)
(* M. Victor Wickerhauser *)
(* 21 May 1990 *)
(* FILTER COEFFICIENTS *)
(* We start with some standard conjugate quadrature filters: *)
stdH[10] = {0.160102397974, 0.603829269797, 0.724308528438,
0.138428145901, -0.242294887066, -0.032244869585,
0.077571493840, -0.006241490213, -0.012580751999,
0.003335725285};
std[12] = { 0.111540743350, 0.494623890398, 0.751133908021, 0.315250351709,
-0.226264693965, -0.129766867567, 0.097501605587, 0.027522865530,
-0.031582039318, 0.000553842201, 0.004777257511, -0.001077301085};
coif[12] = {1.15875967387, -.02932013798, -.04763959031,
.273021046535, .574682393857, .294867193696, -.0540856070917,
-.0420264804608, .0167444101633, .00396788361296,-.00128920335614,
-.000509505399};
sr15 = Sqrt[15.0];
coif[6] = {(sr15-3.0)/32.0,(1.0-sr15)/32.0,(3.0-sr15)/16.0,(sr15+3.0)/16.0,
(sr15+13.0)/32.0,(9.0-sr15)/32.0};
mirrorFilter[ filter_ ] :=
Block[{len},
len = Length[filter];
Table[ (-1)^n filter[[len+1-n]], {n,1,len}]
]
(* CONVOLUTION AND DECIMATION *)
(* Define the convolution decimation operators convolveDecimate[] as a
function of two arguments: filter list, and vector list: *)
convolveDecimate[filter_, vector_]:=
Block[{vectorLength,filterRange},
vectorLength = Length[vector];
filterRange = Length[filter];
Table[
Sum[ filter[[j]] vector[[Mod[2i+j-3,vectorLength]+1]],
{i,1,filterRange}
],
{i,1,vectorLength/2}
]
]
(* The adjoint of this operation is similarly defined: *)
antiConvolve[filter_, vector_]:=
Block[{tempVec, newLength, filterRange, vectorLength},
vectorLength = Length[vector];
filterRange = Length[filter];
newLength = 2 vectorLength;
tempVec = Table[0,{i,1, newLength}]; (* initialize output *)
Do[
tempVec[[ Mod[2j+i-3,newLength]+1 ]] += vector[[j]] filter[[i]],
{j,1,vectorLength},
{i,1,filterRange}
];
tempVec
]
(* MAKING WAVELETS AND WAVELET PACKETS *)
(* Now we can anticonvolve a wavelet of length 512: *)
H = coif[6]; G = mirrorFilter[H];
w1 = antiConvolve[ H,
antiConvolve[ H,
antiConvolve[ H,
antiConvolve[ H,
antiConvolve[ H,
antiConvolve[ G,{1,0,0,0,0,0,0,0}]
]
]
]
]
];
ListPlot[w1,PlotRange->{-.05,.05},PlotJoined->True]
(* Wavelet packets are similarly made with other sequences of filters: *)
wp1 = antiConvolve[ H,
antiConvolve[ G,
antiConvolve[ H,
antiConvolve[ G,
antiConvolve[ G,
antiConvolve[ G,{1,0,0,0,0,0,0,0}]
]
]
]
]
];
ListPlot[wp1,PlotRange->{-.05,.05},PlotJoined->True]
--------------------------- Topic #3 -----------------------------------
From: Ramesh Gopinath <ramesh@dsp.rice.edu>
Subject: Wavelet Papers and MATLAB Software from Rice University.
Wavelet Papers and MATLAB Software from Comp. Math. Lab, Rice University.
Announcing the availability of rice-wlet-tools-1.1, a collection of MATLAB
"mfiles" and "mex" files for twoband and M-band filter bank/wavelet analysis
from the DSP group and Computational Mathematics Laboratory (CML) at Rice
University, Houston, TX.
The programs have been tested on Sparcstations running SUNOS with MATLAB 4.1.
However, the "mex" code is generic and should run on other platforms (you may
have to tinker the Makefiles a little bit to make this work). There are
several utility routines all of them callable from matlab. All the C files
(leading to the mex files) can also be directly accessed from other C or
Fortran code. A collection of of papers and tech. reports from the DSP group
(to be expanded soon to all CML reports) is also available.
You could obtain this distribution of software and papers by anonymous ftp
from cml.rice.edu OR by telnet from dsp.rice.edu or cml.rice.edu. Telnet
should be preferred since it would to insulate the user from any future
system changes at cml or dsp.
1. ANONYMOUS FTP: cml.rice.edu (128.42.62.23)
In directories /pub/dsp/software and /pub/dsp/papers
2. TELNET: dsp.rice.edu (128.42.4.62) or cml.rice.edu (128.42.62.23)
This method of access automatically installs all the files and compiles them
so that you are ready to go.
%telnet dsp.rice.edu 5555 | sed '1,3d' | csh -fsb OPTIONS
OPTIONS is a list of options. You may (for convenience) want to add
alias riceget "telnet dsp.rice.edu 5555 | sed '1,3d' | csh -fsb"
to you .cshrc file so that you may access the software as follows:
%riceget software
for software
%riceget papers
for all papers from the group (as unix compressed postscript files), etc.
%riceget help
would give you a list of available OPTIONS
Report problems/bugs and installation info on non-SUN/non-unix platforms
send mail to wlet-tools@rice.edu (or ramesh@dsp.rice.edu)
ramesh gopinath
dept. of ece., rice university, houston, tx-77251-1892
tel. off.(713)-527-8750 x3569 (or) x3508
tel. home. (713)-794-0274
--------------------------- Topic #4 -----------------------------------
From: Mladen Victor Wickerhauser, Washington University.
Subject: Windows 3.1 implementation of the wavelet fingerprint compression.
This is to announce a free Windows 3.1 implementation of the wavelet-based
FBI standard fingerprint compression algorithm. It can be obtained by
anonymous ftp from:
wuarchive.wustl.edu,
in the directory:
doc/techreports/wustl.edu/math/software
as the file:
wsqwin.zip
This is an archive containing the program and a read.me file which is
partially reproduced below. Use PKUNZIP to unpack the archive once you
download it.
software/wsqwin.zip
TI: WSQ -- the FBI/Yale/Los Alamos [W]avelet-packet [S]calar [Q]uantization
fingerprint compression algorithm, for Windows 3.1 or higher.
AU: He Ouyang and M. Victor Wickerhauser
IN: Washington University in St. Louis
SO: Executable is available by anonymous ftp only
ST: Public software
AB: This is an implementation of the WSQ algorithm as described in ``IAFIS
Use of the Wavelet Scalar Quantization (WSQ) Compression/Decompression
Algorithm,'' J. J. Werner, 8 December 1992. The implementation is designed
for well-equipped IBM-type desktop computers using the Windows 3.1 operating
system. It reads .BMP files and writes standard-format compressed files, and
vice versa. Results are displayable on a high-resolution video monitor. The
quality factor can be set under menu control. Computations are performed in
integer arithmetic -- no floating-point coprocessor is needed.
DE: fingerprints, wavelets, compression, decompression
SC:
MA: wuarchive.wustl.edu
FN: doc/techreports/wustl.edu/math/software/wsqwin.zip
TL: ZIP archive containing executable WSQWIN.EXE and READ.ME
DA: 8 September 1993
Professor Mladen Victor Wickerhauser <victor@math.wustl.edu>
Department of Mathematics, Campus Box 1146, One Brookings Drive,
Washington University in Saint Louis, Missouri 63130 USA
Telephone: USA+(314)935-6771; Facsimile: USA+(314)935-5799
--------------------------- Topic #5 -----------------------------------
From: Vinod Raghavan, School of Chemical Engineering, Oklahoma State University
Subject: Questions
Dear Waveletters,
I need lots of help. First I want to know how to pad a finite length
signal before the decomposition. I have tried the circular convolution
technique and for the Daubechies family of wavelets, it works fine. The
problem creeps up when I am dealing with a signal like a step function.
The decomposition coefficients come out real wierd, more so when I go
down a number of levels. But, if I repeat the same padding procedure
while reconstructing it, I get perfect reconstructions.
My problems is that I am using the decomposition coefficients for Pattern
Recognition purposes and can't afford to get poor coefficients. Perfect
reconstruction is secondary to me , but is important. I tried padding it
using Mallat's procedure in " A theory for multi-resolution signal
decomposition: a wavelet representation" in IEEE Transactions on Pattern
Recognition and Machine Intelligence,Vol.11, No.7 July 1989, but then
the decomposition somehow screws up. Does any one else have this same
problem?
What kind of padding should I use to avoid poor coefficients and
still get perfect reconstruction?
I think this is a critical issue, but none of the articles I have read talk
about this. Have I missed any article?
My second problem: Is there any article in English that deals with the
construction of the Meyer,Battle-Lemarie and other wavelets(other than the
Daubechies and the Biorthogonal wavelets developed by Daubechies) explicitly?
Is there any article where the coefficients for these wavelets are tabulated
for some orders so that I can compare my values with these. As far as I
know only Daubechies has done that. That benefits non-mathematicians like me
a lot.
I would appreciate any help.
Vinod Raghavan.
423 Engineering North, School of Chemical Engineering
Oklahoma State University, Stillwater,OK 74078 USA
Email:vinodr@master.ceat.okstate.edu
--------------------------- Topic #6 -----------------------------------
From: Qu Jin, McMaster University, Canada.
Subject: Preprint available: Wavelet Function, Scaling function and DWT
WAVELET FUNCTION, SCALING FUNCTION AND DISCRETE WAVELET TRANSFORM
Q.Jin, Z.Q.Luo and K.M.Wong
Department of Electrical and Computer Engineering
McMaster University, Hamilton, Ont. Canada L8S 4L7
ABSTRACT:
In this paper, we discuss the very general condition for a function to be a
scaling function and a wavelet function. The necessary and sufficient condition
for the functions to form a multiresolution wavelet decomposition and
reconstruction is presented. Through the investigation of
multiresolution analysis and filter bank theory, the interrelationship between
continuous wavelet transform and discrete wavelet transform is established.
A copy of this paper is available by send your address to
Jin@CRlvax.Eng.Mcmaster.ca
or write to Dr. Qu Jin of the address above.
--------------------------- Topic #7 -----------------------------------
From: Dr. Roland Klees, GeoForschungsZentrum, Potsdam, Germany
Subject: Question: Wavelets on closed surfaces in 3D Euclidean Space?
Dr. Roland Klees
GeoForschungsZentrum (GFZ)
P.O.Box 600751
14407 Potsdam, Germany
Phone: ++49 331-310-243, Fax: ++49 331-310-648
e-mail: klees@gfz-potsdam.de
Question: wavelets on closed surfaces in three-dimensional Euclidean Space?
I look for literature on
1. wavelets on closed surfaces ...
2. solution of boundary integral equations (2D) using wavelets
3. wavelet transform for fast solution of linear systems
4. time series analysis with wavelets
Many Thanks
Roland Klees
--------------------------- Topic #8 -----------------------------------
From: Charles Chui, Texas A&M University.
Subject: ACHA: A new wavelet journal, first issue.
ANNOUNCEMENT: A new wavelet journal.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Time-Frequency and Time-Scale Analysis, Wavelets,
Numerical Algorithms, and Applications (ACHA)
The first issue will appear in Nov. - Dec. 1993. This interdisciplinary
journal is published by Academic Press, Inc. with Charles K. Chui,
Ronald Coifman, and Ingrid Daubechies as editors-in-chief. The other
editors of this journal are: David Donoho, Alexander Grossmann,
Wolfgang Hackbusch, Stephane G. Mallat, Yves F. Meyer, Vladimir
Rokhlin, Alan S. Willsky, Alain Arneodo, Pascal Auscher, Guy Battle,
Gregory Beylkin, Albert Cohen, Wolfgang Dahmen, Marie Farge,
Patrick Flandrin, Leslie F. Greengard, Moshe Israeli, Stephane Jaffard,
Bjorn Jawerth, Iain M. Johnstone, Pierre Gills Lemarie-Rieusset,
W.R. Madych, Charles A. Micchelli, Xianliang Shi, Ph. Tachmichian,
Bruno Torresani, P. P. Vaidyanathan, Martin Vetterli,
Jianzhong Wang, Guido L. Weiss, and M. Victor Wickerhauser.
SUBSCRIPTION RATES:
Institutional Personal
In the U.S.A. and Canada: $184 $74
All other countries: $221 $93
ADDRESS: Academic Press, Inc. 1250 Sixth Ave, San Diego, CA 92101, U.S.A.
AUTHOR INFORMATION:
ACHA is an interdisciplinary journal. It publishes high-quality
papers in all areas related to the applied and computational aspects
of harmonic analysis in a broad sense: theoretical mathematical
developments which are relevant to applications, physics papers which
provide some type of the "new" harmonic analysis tools, electrical
engineering ideas, applied mathematics applications: all are welcome,
and the list is far from exhaustive.
Authors should bear in mind the interdisciplinary nature of the journal
while staying true to their own field and background. In order to reach as
wide an audience as possible, each author is asked to provide a paragraph
(or two) describing, in more general and clear terms, the goal of the paper.
Original papers only will be considered.
Submission of manuscripts. Manuscripts should be written in clear, concise,
and grammatically correct English and should be submitted in quadruplicate (one
original and three photocopies), including four sets of original figures or
good-quality glossy prints, to:
Applied and Computational Harmonic Analysis
Editorial Office
1250 Sixth Ave., 3rd Floor
San Diego, CA 92101
Detailed information for authors can be obtained from this same address.
TABLE OF CONTENTS of Vol. 1 No. 1:
A Wavelet Auditory Model and Data - John J. Benedetto and Anthony Teolis
Bessel Sequences and Affine Frames - Charles K. Chui and Xianliang Shi
Wavelets on the Interval and Fast Wavelet Transforms - Albert Cohen,
Ingrid Daubechies, and Pierre Vial
Unconditional Bases are Optimal Bases
for Data Compression and for Statistical Estimation - David L. Donoho
Diagonal Forms of Translation Operators for the Helmholtz Equation
in Three Dimensions - V. Rokhlin
Fast Numerical Computations of Oscillatory Integrals Related to
Acoustic Scattering I - B. Bradie, R. Coifman, and A. Grossmann
This is the first issue of the 1993-94 volume, with three issues to be
published in 1994. Starting 1995, the journal will publish 4 issues per year.
ABSTRACTS of the above papers can be obtained via ftp in the following
steps:
a) ftp wavelet1.math.tamu.edu
b) USER: achasite
c) password: abstract
d) mget acha11.abstract
--------------------------- Topic #9 -----------------------------------
From: Vinod Raghavan, School of Chemical Engineering, Oklahoma State University
Subject: Question: Calculating the coefficients for the Chui wavelets?
Could some one tell me how to calculate the reconstruction coefficients for
the Chui family of wavelets?
I was able to calculate the scaling function and wavelet coefficients for
that family, but in the computation of the reconstruction coefficients,
there is an infinite length polynomial that has to be dealt with. Infinite
sequences are something I not comfortable with.
I am looking forward to some enlightening mails from math gurus around...
Vinod Raghavan
School of Chemical Engineering
Oklahoma State University
Stillwater,OK 74078
vinodr@master.ceat.okstate.edu Wed Sep 22 08:41:18 1993
--------------------------- Topic #10 -----------------------------------
From: Francoise.Peyrin@imag.fr
Subject: CFP: "Time-frequency, Wavelets and Multiresolution", Lyon, France
"Time-frequency, Wavelets and Multiresolution :
Theory, Models and Applications"
March 9-11, 1994, Lyon, FRANCE.
Announcement and Call for Papers
The French Group of Research in Signal and Image Processing (GdR
TDSI) of CNRS (National Center for Scientific Research) organizes two
"Thematic days" devoted to "Time-frequency, wavelets and multiresolution".
During these days (March 9-10, 1994), invited speakers will present
tutorials on both the theoretical basis and the state of the art in the
domain. The conferences will mainly be presented in French.
A workshop (one day and a half) with contributed papers will
accompany this event. Papers concerning both theoretical aspects or
applications showing the specific interest of these methods are equally
welcome. Particular emphasis will be focused on the convergence of
different approaches : signal / image, time-frequency / time-scale,
wavelets / filter banks, pyramids / multiresolution...
Papers for the workshop can be written and presented either in
French or in English. In any case, the full text of the papers will be
published in the Proceedings and offered to each participant. The number of
participants will be limited.
Papers will be selected by the Program Committee on the basis of a
2-page abstract.
Chairman :
R. Goutte, INSA Lyon, FRANCE
Program Committee :
F. Peyrin, R. Prost, A. Baskurt, P. Flandrin, J.M. Chassery, M. Barlaud
Prelminary list of invited speakers:
J.P. Antoine, M. Barlaud, A. Cohen, P. Flandrin, F. Hlawatsch, M. Kunt, M.
Unser...
Working Calendar :
Deadline for submission of abstracts : October 31, 1993
Selection and replies to authors : December 1st, 1993
Receipt of full papers: January 15, 1994
Registration fees:
Member GdR TDSI Non-Member
Workshop 500 FF 500 FF
Thematic + Workshop 500 FF 800 FF
Days
For further informations, please contact :
Workshop TOM (Time-frequency, Wavelets and Multiresolution)
URA CNRS 1216, Bat 502, INSA Lyon
69621 Villeurbanne Cedex, FRANCE
Tel : (33) 72 43 82 27 Fax : (33) 72 43 85 26
e-mail : tom@cerim.insa-lyon.fr
--------------------------- Topic #11 -----------------------------------
From: Andreas Rieder, Computational Mathematics Laboratory, Rice University.
Subject: Preprints available
The following preprints are available:
1) A WAVELET MULTILEVEL METHOD
FOR DIRICHLET BOUNDARY VALUE PROBLEMS
IN GENERAL DOMAINS
R. Glowinski, A. Rieder, R.O. Wells, X. Zhou
Abstract:
We present a multilevel method for the efficient solution
of the linear system arising from a Wavelet-Galerkin
discretization of a Dirichlet boundary value problem via
a penalty/fictitious domain formulation. The presence of
the penalty term requires a modified coarse grid correction
process in order to guarantee a convergence rate which is
independent of the discretization step size.
Numerical experiments described in the paper confirm the
theoretical results.
Key words: wavelets, multilevel methods, penalty/fictitious
domain formulation, Galerkin methods
Subject classification: AMS(MOS) 65F10, 65N30
Technical Report of the Computational Mathematics Laboratory,
No. CML TR93-06, Rice University, Houston, 1993
2) A WAVELET APPROACH TO ROBUST MULTILEVEL SOLVERS
FOR ANISOTROPIC ELLIPTIC PROBLEMS
A. Rieder, R.O. Wells, X. Zhou
Abstract:
A wavelet variation of the "Frequency decomposition multigrid
method, Part I" (FDMGM) of Hackbusch [Numer. Math. 56, pp.229-245,
1989] is presented.
Our modification allows a deeper analysis of this method. Indeed,
the orthogonality and the multiresolution structure of wavelets
yield the robustness of the additive as well as of the multiplicative
version of the FDMGM relative to any intermediate level. Aspects of
robustness of the multilevel scheme are discussed. Numerical
experiments confirm the theoretical results.
The wavelet version of the FDMGM presented here involves wavelet
packets which have been used before this primarily in signal
processing. As a by-product of our analysis we yield strong Cauchy
inequalities for the wavelet packet spaces with respect to
H^1-inner products.
Key words: wavelets, wavelet packets, robust multilevel methods,
anisotropic problems, Galerkin methods
Subject classification: AMS(MOS) 65F10, 65N30
Technical Report of the Computational Mathematics Laboratory,
No. CML TR93-07, Rice University, Houston, 1993
Compressed postscript copies of these reports are available from
the ftp site cml.rice.edu (128.42.62.23). The files are pub/reports/9306.ps.Z
(first report) or pub/reports/9307.ps.Z (second report).
(login: anonymous, password: your email-address)
Andreas Rieder, Computational Mathematics Laboratory, Rice University,
Houston, Texas 77251, USA
email: rieder@cml.rice.edu
-------------------- End of Wavelet Digest -----------------------------