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

- INTLAB Version 5
- Concepts 2.0.0 Released
- Multi-dimension Interpolation Center
- Prizes Awarded at SIAM Annual Meeting
- Oklahoma City Demographic Analysis Workshops
- Conference at Brown Honoring David Gottlieb
- Staff Position at Applied Mathematics, Inc.
- Postdoctoral Position at University of Erlangen
- Contents, Journal of Approximation Theory
- Subscribe, unsubscribe, change address, or for na-digest archives:
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-------------------------------------------------------

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

elements in the gradient

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/ .

Comments always welcome.

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

decade.

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]),

tutorials and references as well as a downloadable version of

the source code can be found.

If you have questions or are interested in using CONCEPTS,

please do not hesitate to join our mailing list[5].

[1] http://www.concepts.math.ethz.ch/

[2] http://www.opensource.org/docs/definition.php

[3] http://www.opensource.org/licenses/gpl-license.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

check the Updated Investor's Forum page for more information.)

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

(University of Waterloo, Canada)

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,

query, download, analyze, and map Census demographic data for OKC and

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**

Table of Contents: J. Approx. Theory, Volume 127, Number 1, March 2004

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

Table of Contents: J. Approx. Theory, Volume 127, Number 2, April 2004

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

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

Radial basis functions under tension

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

Table of Contents: J. Approx. Theory, Volume 128, Number 1, May 2004

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

Table of Contents: J. Approx. Theory, Volume 128, Number 2, June 2004

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

Table of Contents: J. Approx. Theory, Volume 129, Number 1, July 2004

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

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

End of NA Digest

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