## NA Digest Saturday, August 28, 2004 Volume 04 : Issue 35

Today's Editor:
Cleve Moler
The MathWorks, Inc.
moler@mathworks.com

### Submissions for NA Digest:

Mail to na.digest@na-net.ornl.gov.

Information via e-mail about NA-NET: Mail to na.help@na-net.ornl.gov.

-------------------------------------------------------

From: Siegfried M. Rump <rump@tu-harburg.de>
Date: Mon, 23 Aug 2004 14:41:55 -0000
Subject: INTLAB Version 5

Dear all:

The new Version 5 of INTLAB is available. INTLAB is Matlab toolbox for
self-validating algorithms. Version 5 comprises of
- interval arithmetic for real and complex data including vectors and
matrices (very fast),
- interval arithmetic for real and complex sparse matrices (very fast),
- automatic differentiation (forward mode, vectorized computations,
sparse storage),
- Gradients to solve systems of nonlinear equations,
- Hessians for global optimization,
- automatic slopes (sequential approach, slow for many variables),
- univariate and multivariate (interval) polynomials,
- rigorous real interval standard functions (fast, very accurate, 3 ulps),
- rigorous complex interval standard functions (fast, rigorous, but not
necessarily sharp inclusions),
- rigorous input/output,
- accurate summation, dot product and matrix-vector residuals
(interpreted, but fairly fast)
- multiple precision interval arithmetic with error bounds (does the job,
slow)
and more.

The philosophy of INTLAB is that *everything* is written in Matlab code to
assure best portability.

The new version handles Hessians in pure floating point and with verified
bounds. As an example consider a model problem from

http://www.sor.princeton.edu/~rvdb/ampl/nlmodels/cute/bdqrtic.mod

The function of the model problem to be minimized is
function y = f(x)
N = length(x);
I = 1:N-4;
y = sum( (-4*x(I)+3.0).^2 ) + sum( ( x(I).^2 + 2*x(I+1).^2 + ...
3*x(I+2).^2 + 4*x(I+3).^2 + 5*x(N).^2 ).^2 );

with initial approximation xs=ones(N,1) for N=1000. This means 1e6
and 1e9 elements in the Hessian, or 8 GByte in full storage. In our
implementation Hessians
are stored sparse using a special storage scheme allowing efficient
computations.

The following is executable code to calculate an inclusion of a stationary
point of f by first performing a simple Newton iteration followed by a
verification step for the resulting nonlinear system. Error estimations
are completely rigorous.

>> n = 1000;
xs = ones(n,1);
tic
X = verifynlss(@f,xs,'hSparseSPD');
t = toc
maxrelerr = max(relerr(X))

t =
23.8040
maxrelerr =
5.5992e-013

Inclusions of all components of a stationary point are to some 13 decimal
digits and takes 24 seconds on my 800 MHz Pentium III Laptop. Symmetric
positive definiteness of the Hessian can be verified as well, ensuring a
(local) minimum of f in X.

INTLAB works under Windows, Unix and Mac and is tested under Matlab
Versions 5.3 to 7.0 .
INTLAB is freely available for non-commercial use from

http://www.ti3.tu-harburg.de/~rump/intlab/ .

Best wishes

Siegfried M. Rump

Prof. Dr. Siegfried M. Rump
Inst. f. Computer Science III
Technical University Hamburg-Harburg
Schwarzenbergstr. 95
21071 Hamburg
Germany

------------------------------

From: Philipp Frauenfelder <pfrauenf@math.ethz.ch>
Date: Fri, 27 Aug 2004 22:44:18 +0200
Subject: Concepts 2.0.0 Released

We proudly announce the initial public release of CONCEPTS [1]
under the Open Source[2] license GPL[3]. CONCEPTS is a C++
class library for solving elliptic partial differential
equations (PDEs) numerically.

Design principle of CONCEPTS is the transfer of mathematical
objects and grammar used to specify mathematical and numerical
models of physical systems isomorphically' into simulation
software. Design realization in CONCEPTS uses the C++
functionality of inheritance and derived classes.

Initial design of CONCEPTS and realization of the base classes
in C++ are due to Dr. Christian Lage who has been continuously
involved in design of CONCEPTS at ETH Zurich over the past

The release version of CONCEPTS currently supports hp-Finite
Element Methods in 2D and 3D polyhedra with anisotropic
geometric edge-, vertex- and (inter)face mesh refinements and
arbitrary anisotropic and nonuniform degree distribution for H^1
conforming, hexahedral elements in polygons and polyhedra, for
general second order elliptic systems. Also supported are
discontinuous Galerkin FEM (dGFEM) for linear elements.

Future public releases of CONCEPTS might include wavelet and
generalized Fast Multipole classes for sparse represention of
integral and integrodifferential operators and Polynomial Chaos
classes for the Galerkin solutions of stochastic Partial
Differential Equations; hp-edge element classes for
electromagnetics problems are currently undergoing testing.

We invite you to have a look at the home page of CONCEPTS[1]
were documentation of the classes (generated with Doxygen [4]),
the source code can be found.

If you have questions or are interested in using CONCEPTS,

[1] http://www.concepts.math.ethz.ch/
[2] http://www.opensource.org/docs/definition.php
[4] http://www.stack.nl/~dimitri/doxygen/
[5] https://www.math.ethz.ch/mailman/listinfo/concepts-users

------------------------------

From: Ben Fang <fanginc@gte.net>
Date: Fri, 27 Aug 2004 18:04:51 -0700
Subject: Multi-dimension Interpolation Center

In March and November 2003, we reported our simple, powerful interpolation
method for multi-dimensional space at http://www.fanginc.com/main.htm.
The method can be applied to arbitrary dimensions (1D, 2D, 3D, ...10D,....)
in terms of Cartesian coordinates.

Today, more calculations are posted at the same web site. They include:

(1) Numerical comparison in 2-dimension with two best known interpolation
methods (Shepard's and Hardy's) and the graphical presentation of "smoothness";
(2) Numerical results of reproduced function value and cross-validation in
4-dimension;
(3) Updated FAQ page which includes the web-link to the revised study of
"accuracy and convergence" of our method;
(4) Interpolant formulas derived analytically for non-Cartesian coordinates,
polar (2D), spherical (3D) and cylindrical (3D) coordinates; (They have been
incorporated in a new proposal submitted to NSF for funding support. Please

Feedbacks are most welcome. Critical comments from the computing community
are appreciated.

Dr. Ben K.K. Fang
FANG, INC.
fanginc@gte.net

------------------------------

From: A. G. Bogardo <bogardo@siam.org>
Date: Tue, 24 Aug 2004 12:59:26 -0400
Subject: Prizes Awarded at SIAM Annual Meeting

Following are the recipients of prizes awarded at the SIAM Annual Meeting held
last month in Portland. For further details on these awards, please visit
http://www.siam.org/prizes/an04booklet.htm.

I. E. Block Community Lecture, intended to encourage public appreciation
of the excitement and vitality of applied mathematics:

Michael B. Ray
ExxonMobil Upstream Research Company

Richard C. DiPrima Prize, awarded to a young scientist who has done
outstanding research in applied mathematics, based on the doctoral
dissertation:

Diego Dominici
SUNY-New Paltz

AWM-SIAM Sonia Kovalevsky Lecture, intended to highlight significant
contributions of women to applied or computational mathematics:

Joyce R. McLaughlin
Rensselaer Polytechnic Institute

SIAM Outstanding Paper Prizes, awarded for three outstanding papers
published in SIAM journals during the three years prior to the award:

Gerard Cornuejols (Carnegie Mellon University) and Bertrand Guenin

Feimin Huang (Academia Sinica, Beijing, China) and Zhen Wang (City
University of Hong Kong, China)

Alfio Quarteroni (Politecnico di Milano, Italy), Alessandro
Veneziani (EPFL, Switzerland and Politecnico di Milano), and Paolo
Zunino (EPFL, Switzerland)

George Polya Prize, awarded for a notable application of combinatorial
theory:

Neil Robertson
The Ohio State University

Paul Seymour
Princeton University

W. T. and Idalia Reid Prize in Mathematics, for outstanding work in, or
other contributions to, the broadly defined areas of differential
equations and control theory:

Arthur J. Krener
University of California, Davis

SIAM Award in the Mathematical Contest in Modeling (MCM), awarded to two
of the teams judged "Outstanding" in the annual MCM:

Steven Avery, Eric Harley, Eric Malm (Faculty Advisor: Jon T.
Jacobsen) Harvey Mudd College

Moorea Brega, Alejandro Cantarero, Corry Lee (Faculty Advisor: Bengt
Fornberg) University of Colorado at Boulder

SIAM Prize for Distinguished Service to the Profession, awarded to an
applied mathematician who has made distinguished contributions to the
furtherance of applied mathematics on the national level:

Richard A. Tapia
Rice University

SIAM Student Paper Prizes, awarded to the student authors of the most
outstanding papers submitted to the SIAM Student Paper Competition:

Silas D. Alben, Courant Institute of Mathematical Sciences, New York
University

Alfonso Bueno Orovio, University of Castilla-La Mancha

Martin Kleinsteuber, University of Wuerzburg

Theodore von Karman Prize, awarded for a notable application of
mathematics to mechanics and/or the engineering sciences:

Roland Glowinski
University of Houston

The John von Neumann Lecture, awarded to a mathematician (or to a
scientist in another field) who has made distinguished contributions to
pure and/or applied mathematics:

Alan C. Newell
University of Arizona

------------------------------

From: Gina Clemmer <info@sgtinfo.com>
Date: Fri, 27 Aug 2004 09:47:46 -0700
Subject: Oklahoma City Demographic Analysis Workshops

Oklahoma City Demographic Analysis Workshop

When: September 9th and 10th, 2004 - 9:00 am to 4:00 pm (One Day
Workshop. Participants may choose either day.)
Where: New Horizons Computer Training Center, 50 Penn Place, 1900 NW
Expressway, Suite R305 Oklahoma City, Oklahoma 73118
Fee: $225 w/credit card at time of registration,$249 for check or
purchase order after workshop Register Now

Register online at www.sgtinfo.com or call us at 877.241.6576.
The Oklahoma City Demographic Analysis Workshop will teach you to extract,
surrounding communities. (Note: Participants may substitute their own
community in exercises-all techniques are directly transferable to other
communities). Such data can provide grant writers, social researchers and
community planners with powerful tools for analyzing community changes.

------------------------------

From: Wei Cai <wcai@uncc.edu>
Date: Fri, 27 Aug 2004 12:58:41 -0400
Subject: Conference at Brown Honoring David Gottlieb

International Conference on the Research Trend for PDE Modeling and
Computation

On the Occasion of Prof. David Gottlieb's 60th Birthday
Brown University
November 7-8, 2004

Conference program and registration information are posted at the website

http://www.math.uncc.edu/gottlieb/

There is no registration fee, however, an e-mail registration to
wcai@uncc.edu is required for participation.

------------------------------

From: William J. Browning <wjb@applmath.com>
Date: Tue, 24 Aug 2004 13:14:52 -0400
Subject: Staff Position at Applied Mathematics, Inc.

Numerical Analyst Position at Applied Mathematics, Inc.

Numerical Analyst needed to work with physicists and mathematicians
developing computer models of physical systems and associated applications
software. Applications include submarine tactical detection and tracking
systems, flow control, remote sensing and pharmaceuticals. Clients include
U.S. Navy, government research facilities and private industry.

Strong research, extensive computer, and excellent communications skills
are required. Ph.D. and U.S. citizenship are required.

Send resumes to: William J. Browning
E-mail: wjb@applmath.com

------------------------------

From: Ulrich Ruede <ruede@immd10.informatik.uni-erlangen.de>
Date: Tue, 24 Aug 2004 11:58:22 +0200
Subject: Postdoctoral Position at University of Erlangen

At the University of Erlangen-Nuernberg we have an opening for a full
time post-doc associated with our Graduate Program in Computational
Engineering. This position requires fluency in German so that the rest
of this text will be in German.

Am Institut fuer Informatik der Friedrich-Alexander Universitaet
Erlangen-Nuernberg ist zum 1.11.2004 die Stelle eines

Wissenschaftlichen Assistenten/ Assistentin (C1)

als Koordinator/Koordinatorin der Bavarian Graduate School in
Computational Engineering im Elitenetzwerk Bayern zunaechst auf drei
Jahre befristet zu besetzen.

Zu den Aufgaben gehoert die Betreuung der Studierenden in dem ab WS
2004/05 gemeinsam mit der Technischen Universitaet Muenchen
betriebenen Elite-Masterstudium, sowie die Beteiligung an der Lehre
und die standortuebergreifende Koordination des Lehrangebots.
Voraussetzung sind ein Studium in einem
mathematisch-naturwissenschaftlichen oder technischen Fach, eine
einschlaegige Promotion und Erfahrung im Gebiet "Computational Science
and Engineering". Die Stelle erfordert ein besonderes Engagement in
der Lehre sowie Team- und Kommunikationsfaehigkeit. Die Moeglichkeit
zur Weiterqualifikation ist gegeben. Naehere Information zu der
ausgeschriebenen Stelle ist im Internet verfuegbar unter
http://www10.informatik.uni- erlangen.de/~ruede/

------------------------------

From: Thomas Hogan <hogan@math.ohio-state.edu>
Date: Fri, 27 Aug 2004 13:41:25 -0400 (EDT)
Subject: Contents, Journal of Approximation Theory

Online at www.sciencedirect.com/science/issue/6843-2004-998729998-498852

T. Kasuga and R. Sakai
Orthonormal polynomials for generalized Freud-type weights and
higher-order Hermite-Fej\'{e}r interpolation polynomials
1--38

P\'{e}ter Simon
$(C,\alpha)$ summability of Walsh-Kaczmarz-Fourier series
39--60

Maura Salvatori and Paolo M. Soardi
Multivariate tight affine frames with a small number of generators
61--73

Pedro Ter\'{a}n
Function-valued Korovkin systems without quasiconcavity and set-valued
Korovkin systems without convexity
74--82

Ana Portilla, Yamilet Quintana, Jos\'{e} M. Rodrmguez, and Eva Tourms
Weierstrass' theorem with weights
83--107

Lars Filipsson
Kergin interpolation in Banach spaces
108--123

David P\'{e}rez-Garc\'{\i}a and Ignacio Villanueva
Where do homogeneous polynomials on ${\ell_1}^n$ attain their norm?
124--133

E. Belinsky, F. Dai, and Z. Ditzian
Erratum to Multivariate approximating averages''
[J.~Approx.\ Theory 125 (2003) 85--105]
134

Online at www.sciencedirect.com/science/issue/6843-2004-998729997-501577

A. Bouhamidi and A. Le M\'{e}haut\'{e}
135--154

H. S. Jung
Estimates for the first and second derivatives of the
Stieltjes polynomials
155--177

Heinz H. Bauschke, Patrick L. Combettes, and D. Russell Luke
Finding best approximation pairs relative to two closed convex sets in
Hilbert spaces
178--192

Xinghua Wang, Ming-Jun Lai, and Shijun Yang
On the divided differences of the remainder in polynomial interpolation
193--197

Grzegorz Lewicki and Michael Prophet
Codimension-one minimal projections onto Haar subspaces
198--206

Semyon Rafalson
On constants in some inequalities for intermediate derivatives on a
finite interval
207--222

B. Della Vecchia, G. Mastroianni, and J. Szabados
Weighted approximation of functions on the real line by
Bernstein polynomials
223--239

Paul Nevai and Vilmos Totik
Denisov's theorem on recurrence coefficients
240--245

Author index for Volume 127
246

Online at www.sciencedirect.com/science/issue/6843-2004-998719998-503643

Ben-yu Guo and Li-lian Wang
Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
1--41

Ingo Steinwart
Entropy of convex hulls---some Lorentz norm results
42--52

Andreas Defant, Domingo Garcma, and Manuel Maestre
Estimates for the first and second Bohr radii of Reinhardt domains
53--68

Gy\"{o}rgy G\'{a}t
On the pointwise convergence of Ces\{a}ro means of two-variable
functions with respect to unbounded Vilenkin systems
69--99

Chelo Ferreira
A note on the error bound for the remainder of an asymptotic expansion
of the double gamma function
100--101

Online at www.sciencedirect.com/science/issue/6843-2004-998719997-505987

Chin-Cheng Lin and Kunyang Wang
Convergence rate of Fourier-Laplace series of $L^2$-functions
103--114

Hans-J\"{u}rgen Schmeisser and Winfried Sickel
Spaces of functions of mixed smoothness and approximation from
hyperbolic crosses
115--150

Dorothee D. Haroske and Susana D. Moura
Continuity envelopes of spaces of generalised smoothness, entropy and
approximation numbers
151--174

K. H. Kwon and D. W. Lee
Inequalities of Rafalson type for algebraic polynomials
175--186

Dietrich Braess and Thomas Sauer
Bernstein polynomials and learning theory
187--206

Werner Linde
Kolmogorov numbers of Riemann-Liouville operators over small sets and
applications to Gaussian processes
207--233

Author index for Volume 128
234

Online at www.sciencedirect.com/science/issue/6843-2004-998709998-509316

Hans Triebel
Approximation numbers in function spaces and the distribution of
eigenvalues of some fractal elliptic operators
1--27

Simon Hubbert and Tanya M. Morton
A Duchon framework for the sphere
28--57

Simon Hubbert and Tanya M. Morton
$L_p$-error estimates for radial basis function interpolation on
the sphere
58--77

Deguang Han
Tight frame approximation for multi-frames and super-frames
78--93

D. G. Kubayi and D. S. Lubinsky
A Hilbert transform representation of the error in Lagrange interpolation
94--100

Ying Guang Shi
Erratum to `Convergence of Hermite-Fej\'{e}r type interpolation of
higher order on an arbitrary system of nodes''
[J.~Approx.\ Theory 123 (2003) 173--187]
101

Ying Guang Shi
Convergence of Hermite-Fej\'{e}r type interpolation of higher order on
an arbitrary system of nodes
102--117

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End of NA Digest

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