## NA Digest Sunday, March 10, 2002 Volume 02 : Issue 10

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: Luis Almeida <luis.almeida@inesc-id.pt>
Date: Mon, 04 Mar 2002 17:06:48 +0000
Subject: Help with Ordinary Differential Equation

Dear colleagues,

A brother of mine, who works on physics, needs to find solutions of the
following differential equation (in Mathematica notation):

x^4 y''[x] y[x] == -1

He needs solutions that are real at least for some values of x, and that
are as general as possible. Until now he knows a pair of solutions which
are imaginary:

y[x] = I Sqrt[2]/(2 x) and its symmetrical.

We've found solutions of equations which are somewhat similar to the
original one, and which might give an indication of the kind of form the
solutions of the original equation might have.

The equation y''[x] y[x] == -1 has solution

y[x] = Sqrt[2/Pi] 1/a Exp[-(InverseErf[a (x-b)])^2]

with a and b arbitrary constants.

The equation x^2 y''[x] y[x] == -1 has solution

y[x] = Sqrt[2/Pi] 1/a x Exp[-(InverseErf[a/x])^2]

with a an arbitrary constant. Since the equation is of second order,
this shouldn't be the most general form of the solution.

Any help is greatly appreciated.

Just to give you an idea of where this problem comes from, this is part
of the solution of a certain wave equation. The solution has a factor
dependent on the distance from the origin, and another factor dependent
on angles. Here, y is the inverse of the radial factor, and x is the
inverse of the radius. Using these inverses allowed a significant
simplification of the form of the equation.

Luis B. Almeida
Phone: +351-213100246
INESC-ID Fax: +351-213145843
R. Alves Redol, 9 E-mail: luis.almeida@inesc-id.pt
1000-029 Lisboa, Portugal http://neural.inesc-id.pt/~lba/

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

From: Kartikkrishnan Sivaramakrishnan <kartis@rpi.edu>
Date: Thu, 7 Mar 2002 23:35:26 -0500
Subject: Diagonal Perturbation of an Indefinite Matrix

Hello all,

I have the following problem. I am given an indefinite matrix G. I want
to find a diagonal perturbation E, s.t. G+E is positive semidefinite [psd].

i.e. find a diagonal perturbation E, that is "as small as possible" s.t.

G + E is positive semidefinite, where G by itself is indefinite. All
matrices are of size n.

A few points here :-

(i) I know this problem can be formulated as a semidefinite programming
problem [SDP] to find the optimal E, but I want something much cheaper.
Actually, I need this to update my upper bounds in a cutting plane approach,
and I am looking for something cheap and dirty.
(ii) Currently the best E , I could come up with is E = lambda I, where
lambda is the absolute value of the most negative eigenvalue of G, and I is
the identity matrix of the appropriate size. Note that this choice for E
ensures that G+E is positive semidefinite.
(iii) My question is whether one could come up with a better diagonal
matrix E such that trace(E) <= trace(lambda I) = n*lambda. This will give
me the desired 'lower' upper bound.
(iv) I had a look at a number of Modifed Cholesky factorization schemes
[Gill, Murray, Wright], [Schnabel, Esknow], but these are not directly
applicable to my problem, since they give a diagonal E, such that
G+E is positive definite [not positive semidefinite], besides
||E|| is usually much greater than the absolute value of the most negative
eigenvalue of G.

To summarize, my question is whether it is possible to come up with
a diagonal E, such that trace(E) <= n*lambda [with lambda defined as above],
without solving an SDP?

Comments, suggestions, and pointers to any existing software would be
welcome.

Thank you.

Sincerely,
Kartik

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

From: Austin Dubrulle <adubrulle@worldnet.att.net>
Date: Sun, 10 Mar 2002 19:02:50 -0800
Subject: Olin Johnson Publishes Historical Novel

Just to show that numerical analysts are people of many talents---as if
that were necessary.

Our colleague and friend Olin Johnson (University of Houston) has
recently published a historical novel, "The Newlanders," based on his
family genealogy. It starts in the eighteenth century with David
Jansohn's journey from Germany to America---and ends in 1968 with
a Galerkin solution of the Sturm-Liouville problem at UC Berkeley
(just kidding; not part of the book).

Historical novel is a challenging genre that demands massive research
for historical accuracy (another sort of epsilon). Customers rate the
book at 4+ stars on the Amazon and Barnes & Noble web sites for style
and content.

Good show, Olin!

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

From: Allison Bogardo <bogardo@siam.org>
Date: Tue, 05 Mar 2002 07:36:17 -0500
Subject: SIAM Student Paper Prizes

Deadline Near for SIAM Student Paper Prize Competition

Principal Guidelines

The SIAM Student Paper Prizes are awarded every year to the
student author(s) of the most outstanding paper(s) submitted
to the SIAM Student Paper Competition. This award is based
solely on the merit and content of the student's
contribution to submitted paper(s).

The purpose of the Student Paper Prizes is to recognize
outstanding scholarship by students in applied mathematics
or computing.

Selection Procedures

Eligibility

Eligibility is restricted to students in good standing who
have not received their Ph.D. at the time of submitting
their entry or who have completed their degree within one
year of submission of their entry.

Submissions may be based on co-authored papers, provided
that the student's advisor will attest that the student's
work played a pivotal role in the results.

A letter from the student's advisor or department chair must
accompany each entry to verify these conditions.

To enter the competition, a student must submit: (1) an
extended abstract in English of a paper, and (2) a short
biography. The total length of the submitted abstract
(including bibliography) may not exceed five pages. The
student also must submit the complete paper that will be
used for clarification of any questions the selection
committee may have on the extended abstract. In addition,
the student's advisor or an interested faculty member must
submit a letter describing and evaluating the paper's
contribution to the literature, and the student's role in
the scholarship.

For the 2002 award, all papers and accompanying
documentation must be received at the SIAM office by
March 15, 2002.

Notification of Prize Winner

The SIAM president will notify the recipient(s) at least six
weeks before the award date.

Each recipient is required to present his or her paper at
the meeting where the prizes are awarded; if attending
the meeting poses a serious hardship, an exception may be
granted by the SIAM president.

Description of the Award

Each recipient of the SIAM Student Paper Prize shall receive
a framed certificate and a cash award of \$1,000, plus \$500 toward
travel expenses.

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

From: Arieh Iserles <A.Iserles@damtp.cam.ac.uk>
Date: Mon, 4 Mar 2002 10:41:46 GMT
Subject: Conference in Minneapolis on Foundations of Computational Mathematics

Second Announcement & Call for Registration
FOUNDATIONS of COMPUTATIONAL MATHEMATICS CONFERENCE
Minneapolis, 5-14 August 2002

The next Foundations of Computational Mathematics conference will be
held at University of Minnesota on 5-14 August 2002, as guests of the
Institute for Mathematics and its Applications.

The conference, organised by Society for Foundations of Computational
Mathematics, is next in a sequence that commenced with Park City, Rio
de Janeiro and Oxford FoCM meetings. The format will be similar:
plenary invited lectures in the mornings, theme-centred parallel
workshops in the afternoons. Each workshop will be go on for three
days and the conference will consist of three `periods', comprising of
different themes.

PLENARY SPEAKERS:

Ian ANDERSON (Utah State) Teresa KRICK (Buenos Aires)
Philippe CIARLET (Paris 6) Pierre Louis LIONS (Paris 9)
Albert COHEN (Paris 6) Dan LOZIER (NIST)
Tony DeROSE (Pixar) Volker MEHRMANN (TU Berlin)
Herbert EDELSBRUNNER (Duke) Andrew ODLYZKO (Minnesota)
Michael FREEDMAN (Microsoft) Edriss TITI (UC Irvine)
Wolfgang HACKBUSCH (Kiel) Mike TODD (Cornell)
Stefan HEINRICH (Kaiserslautern) Vladimir VAPNIK (AT&T Research)
Pascal KOIRAN (ENS Lyon) Grace WAHBA (Wisconsin)

The overall oversight of FoCM'02 is the responsibility of the FoCM
Executive Committee whose current Chair is Ron DeVORE (University
of South Carolina). The organisation is managed by the Local
Organising Committee: Carme CALDERER, Bernardo COCKBURN, Jianhong
(Jackie) SHEN, Willard MILLER, Peter OLVER and Victor REINER.

WORKSHOPS and their organisers:
* Foundations of numerical PDEs
Philippe Ciarlet (Paris 6), Mitch Luskin (Minnesota) & Eitan Tadmor (UCLA)
* Geometric integration and computational mechanics
Debra Lewis (UC Santa Cruz) & Hans Munthe-Kaas (Bergen)
* Information-based complexity
Erich Novak (Jena), Greg Wasilkowski (Lexington) & Henryk
Wozniakowski (Columbia & Warsaw)
* Learning theory
Tomaso Poggio (MIT) & Steve Smale (UC Berkeley)
* Optimization
Michael Overton (NYU), Bill Pulleyblank (IBM Yorktown Heights) & Jim
Renegar (Cornell)
* Special functions
Tom Koornwinder (Amsterdam) & Adri Olde Daalhuis (Edinburgh)
* Approximation theory
Allan Pinkus (Haifa) & Amos Ron (Madison)
* Computational algebraic geometry
Askold Khovanskii (Toronto) & Teresa Krick (Buenos Aires)
* Computational number theory
Richard Brent (Oxford), Dennis Hejhal (Minnesota & Uppsala) & Carl
Pomerance (Bell Labs)
* Multiresolution and adaptivity in numerical PDEs
Wolfgang Dahmen (Aachen), Raytcho Lazarov (Texas A&M) & Endre S

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

From: Stephane Gerbi <Stephane.Gerbi@univ-savoie.fr>
Date: Sat, 9 Mar 2002 12:29:32 +0100
Subject: Conference in Chambery on Shallow Water Equations

SECOND SAVOISIENNES DAYS OF APPLIED MATHEMATICS

SHALLOW WATER AND SAINT-VENANT EQUATIONS.
THEORY AND APPLICATIONS

to be held 16-17 May 2002 at:
University of Savoie, Campus Scientifique, Le Bourget du Lac, France

Organised by C. Bourdarias, S. Gerbi, M. Gisclon
from the Mathematics Department of the Universty of Savoie, Chambery, France,
with support from Ecole Normale Superieure, PARIS and INRIA Rocquencourt.

List of Speakers:

M.O. BRISTEAU, (INRIA Rocquencourt),
T. GALLOUET, (University of Marseille),
N. GOUTAL, (EDF Paris),
Shi JIN, (University of Wisconsin-Madison),
S. KARNI, (University of Michigan),
D. LAIGLE, (Cemagref Grenoble,
A.Y. LE ROUX, (University of Bordeaux),
D. LEVY, (Stanford University),
M. NAAIM, (Cemagref Grenoble),
G. RUSSO, (Universit=E0 di Catania, Italy)
E. VAZQUEZ, (Universidade de Santiago de Compostela, Spain).

The program of these Days will include 11 invited 1 hour lectures.
Posters presentation by young researchers is also organised.

There are NO registration fees but the inscription is highly recommended
on the on-line registration page of the web site:

http://www.lama.univ-savoie.fr/jsma2002.

For more information send e-mail to: JSMA02@univ-savoie.fr
or consult the Web site: http://www.lama.univ-savoie.fr/jsma2002

Kindly inform your colleagues interested in this field.

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

From: Stephane Lanteri <Stephane.Lanteri@sophia.inria.fr>
Date: Fri, 08 Mar 2002 14:18:47 +0100
Subject: Postdoctoral Position at INRIA Sophia Antipolis

Postdoctoral position in biomedical engineering at INRIA Sophia
Antipolis

Applications are invited for a 12 month postdoctoral position
(starting September 2002) at INRIA Sophia Antipolis. This position is
supported by the multidisciplinary project ICEMA (standing for Images
of the Cardiac Electro-Mechanical Activity) which is a collaborative
research action between different INRIA teams from several INRIA
sites. Informations concerning INRIA, INRIA Sophia Antipolis and the
ICEMA project can be found at the URLs:

- http://www.inria.fr/inria/index.en.html=20
- http://www.inria.fr/inria/organigramme/fiche_ur-sop.en.html=20
- http://www-rocq.inria.fr/who/Frederique.Clement/icema.html=20

An important goal of the ICEMA project is to design an interactive
deformable model that can be used in a clinical context. For this
purpose, this ``Beating Heart Model'' has to be optimized both on the
numerical level (efficiency of linear system solvers) and on the
computer science level (adaptation to parallel architectures). For
the current version of this model, the total computation time for a
full heart beat is around 10 minutes. Ultimately, this computation
time should be decreased to a few seconds. The existing version of
this model consists in a sequential software extensively based on
object oriented pogramming (the software is written in C++). In this
context, the candidate will conduct research and development
activities for:

- the design and implementation of an appropriate parallelization
strategy,

- the interfacing of the software with a (public domain) linear
algebra library that will provide access to efficient (parallel)
iterative solvers and the selection of appropriate methods based on
the mathematical properties of the algebraic systems under
consideration.

The candidate will conduct research and development activities in
collaboration with researchers from the Epidaure
(http://www.inria.fr/recherche/equipes/epidaure.en.html) and Caiman
(http://www.inria.fr/recherche/equipes/caiman.en.html) teams.

The background required from a young researcher wishing to apply for
this position is a PhD in Applied Mathematics or Scientific Computing,
with a strong personal interest in numerical methods and scientific
computing. The ideal candidate should have experience in the
following areas: mathematical and numerical analysis of systems of
partial differential equations using the finite element method,
solving of sparse linear systems of equations using iterative methods
(essentially, preconditioned Krylov methods), object oriented
programming, parallel computing. A working knowledge of C++ is
mandatory. A background in medical research or bioengineering would
be an asset.

This position is open to candidates of any nationality and selection
will be based upon the candidate's area of interest and research
potential.

Candidates should send a CV, including a statement of research
interests, a list of publications and addresses of three references by
June 30, 2002 to:

- Nicholas Ayache (head of Epidaure team)
E-Mail: Nicholas.Ayache@inria.fr

- Herve Delingette (researcher in the Epidaure team)
E-Mail: Herve.Delingette@inria.fr

- Stephane Lanteri (researcher in the Caiman team)
E-Mail: Stephane.Lanteri@inria.fr

More details at the URL:
http://www-rocq.inria.fr/sosso/icema2/icema2.html

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

From: Nathan Baker <nbaker@chemcca33.ucsd.edu>
Date: Wed, 6 Mar 2002 09:55:26 -0800
Subject: Postdoctoral Position at Washington University School of Medicine

Postdoctoral Researcher
Multiscale Simulation of Biomolecular Systems
Washington University School of Medicine
St. Louis, Missouri

A vacancy exists for a postdoctoral researcher in the Department of
Biochemistry and Molecular Biophysics at Washington University
School of Medicine, beginning as early as September 1, 2002. The
position involves the development and application of computational
methods for the multiscale modeling of large biomolecular systems.
Research will be conducted in the laboratory of Nathan A. Baker
(http://wasabi.ucsd.edu/), who will be joining the Washington
University School of Medicine as an Assitant Professor in the summer
of 2002.

Due to the interdisciplinary nature of the research, applications
from all areas of computational science are welcome. However,
candidates must have a Ph.D. (or equivalent), a strong research
background, and a good command of written and spoken English.
Interested applicants should reply via email to
nbaker@wasabi.ucsd.edu. Please attach a current CV with the names
of at least three references and a brief statement of research
background and interests.

Washington University is an equal opportunity employer.

Thank you for your help.

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

From: Lester Ingber <ingber@ingber.com>
Date: Thu, 7 Mar 2002 16:15:51 -0500
Subject: Financial Engineer Position

If you have very strong credentials for the position described below,
Lester Ingber <ingber@ingber.com> Director R&D

Financial Engineer

A disciplined, quantitative, analytic individual proficient in
prototyping and coding (such as C/C++, Maple/Mathematica, or
Visual Basic, etc.) is sought for financial
engineering/risk:reward optimization research position with
established Florida hedge fund (over two decades in the
business and \$1 billion in assets under management). A PhD in a
mathematical science, such as physics, statistics, math, or
computer-science, is preferred. Hands-on experience in the
financial industry is required. Emphasis is on applying
state-of-the-art methods to financial time-series of various
frequencies. Ability to work with a team to transform
ideas/models into robust, intelligible code is key. Salary:
commensurate with experience, with bonuses tied to the
individual's and the firm's performance. Start date for this
position may range anywhere from immediately to six months
hence, depending on both the candidate's and the firm's needs.