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

- A Query About Matrices and Eigenvalues
- Stability in Runge-Kutta-Nystrom
- Results on Conjugate Gradient Method
- Transformation of a Hessian or Covariance Matrix
- DAEPACK Version 1.0 Announcement
- SIAM Annual Meeting
- Meeting on Pseudospectra of Random Nonhermitian Matrices
- Sino-Japan Optimization Meeting
- Department Head Position at Memorial University
- Faculty Position at Lund Institute of Technology
- Postdoctoral Position at ENSGTI, Pau, France
- PhD Position at EPFL
- PhD Position at Institut Francais du Petrole, Paris
- Visiting Positions at Swiss Center for Scientific Computing

**URL for the World Wide Web:**
http://www.netlib.org/na-net/na_home.html

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

From: Francois Robert <Francois.Robert@imag.fr>

Date: Sun, 12 Mar 2000 21:04:56 +0100

**Subject: A Query About Matrices and Eigenvalues**

Let M be a nonsingular n by n matrix. Set A = M'*M , and take for simplicity

the columns of M of Euclidean norm 1. Then diag(A) = I.

It is easy to prove that:

* the eigenvalues of A belong to the open interval (0, n)

* Moreover, if A is tridiagonal, then its eigenvalues belong to (0,2)

(a little bit harder, since a crude localization gives (0,3) )

Question: Is it possible to derive similar localizations when A is

pentadiagonal, heptadiagonal, and so on? One should get (0, n) for a full A .

Thanks a lot for any help!

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

From: Amelia Garcia <amegar@eis.uva.es>

Date: Fri, 17 Mar 2000 09:51:26 +0100

**Subject: Stability in Runge-Kutta-Nystrom**

I am writing to ask for information on absolute stability in

Runge-Kutta-Nystrom methods. I should be very greatful if someone sends

me references about this.

Amelia Garcia

Dpto. de Matematica Aplicada a la Ingenieria

E.T.S. de Ingenieros Industriales

Universidad de Valladolid

Paseo del Cauce s/n

47011-Valladolid, Spain

e-mail: amegar@eis.uva.es

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

From: Aloke Phatak <Aloke.Phatak@cmis.CSIRO.AU>

Date: Sun, 19 Mar 2000 13:14:18 +0800

**Subject: Results on Conjugate Gradient Method**

There are lots of results scattered throught the literature on the

Conjugate Gradient method, but I've yet to come across any results on the

Euclidean norms of the iterates themselves. In particular, is there an

explicit proof of the result that when solving Ax = b with A (n x n)

symmetric positive definite and initial estimate x(0) = 0,

||x(1)|| < ||x(2)|| < ... < ||x(n)|| ?

Any pointers to the literature would be much appreciated.

My interest stems from the fact that for x(0) = 0, CG is identical to a

widely used estimator of the parameters in linear regression know as

the "partial least squares" estimator. In statistical parlance, it is

a shrinkage estimator, but existing proofs of its shrinkage properties

are somewhat cumbersome.

Aloke Phatak

CSIRO Mathematical and Information Sciences .

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

From: Ken Turkowski <turk@mail.apple.com>

Date: Wed, 8 Mar 2000 01:40:44 -0800

**Subject: Transformation of a Hessian or Covariance Matrix**

I'm transforming one image via a projective transformation to another,

attempting to find the best parameters for the projective transformation

by means of least squares optimization (Levenberg-Marquardt). In order to

increase the stability of the optimization (i.e. to make the error

landscape "rounder" instead of oblong), I convert the coordinate system

so that the origin is at the center of the images, and I scale the images

so that the pixel coordinates go from -1 to +1 (instead of

[0,767]x[0,512]). A multi-resolution pyramid is used for the

registration, so there is a coordinate change between the levels of the

pyramid as well.

__

M* = arg min \ e(p)^2

M /_

p in omega

e(p) = I0(p) - W(I1; p, M)

where

M is a vector of parameters for the projective transformation

p is the coordinates of a pixel

omega is the overlap region between the first image and the

transformed second one

I0() and I1() are two images

W() is an image warping function

The Taylor series expansion at M is given by

1

E(M + a) = E(M) + G . a + _ a^t . H . a + ...

2

where

d E

G = ___ is the gradient of E with respect to the warp parameters M

d M

d^2 E

H = _________ is the Hessian

d Mi d Mj

At the optimum, the gradient is essentially zero (ignoring inevitable

noise), and the error is some finite number, and error landscape in the

neighborhood of the optimum is described by the Hessian:

1

E(M* + a) =~ E(M*) + _ a^t H a

2

The Hessian is either supplied or computed in many optimization schemes

(e.g. supplied in Levenberg-Marquardt, computed in BFGS, but not used at

all in conjugate gradient).

The transformation of the projective transformation from the stabilized

coordinate system to the standard upper-left integral image coordinate

system is given by:

| Sl 0 Cxl | | Sr 0 Cxr | -1

M' = | Sl Cyl | . M . | 0 Sr Cyr |

| 0 0 1 | | 0 0 1 |

where the S's are scale factors, and the C's are offsets, and the

projective transformation M is represented in matrix form

| m00 m01 m02 |

M = | m10 m11 m12 |

| m20 m21 1 |

such that

m00 * x + m01 * y + m02

x' = _______________________

m20 * x + m21 * y + 1

m10 * x + m11 * y + m12

y' = _______________________

m20 * x + m21 * y + 1

performs the perspective transformation.

The question is how to transform the Hessian?

Perhaps the real question is:

What is the appropriate chain rule for second derivatives for scalar

functions of vector variables?

Or, more to the point,

Given the Taylor expansion of a function of several variables

E(m + a) = E(m) + G(m) . a + a^t . H(m) . a

and a transformation of parameters

m = t(n)

what is the Taylor expansion

E(t(n + b))

Ken Turkowski

Immersive Imaging Technologist

Apple Computer, Inc.

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

From: Paul Barton <pib@MIT.EDU>

Date: Mon, 13 Mar 2000 14:56:30 -0500

**Subject: DAEPACK Version 1.0 Announcement**

ANNOUNCING DAEPACK VERSION 1.0

The Massachusetts Institute of Technology is pleased to announce the

availability of DAEPACK version 1.0 for academic and commercial uses

licensing.

DAEPACK is a symbolic and numeric library for general numerical

calculations. What distinguishes DAEPACK from other software libraries for

numerical computations is a set of symbolic components that operate

directly on very general Fortran-90 code provided by the user. The

symbolic components take as input a set of Fortran-90 source files defining

a system of equations of interest and generate a new set of Fortran-90

subroutines and functions computing quantities such as analytical

derivatives matrices, sparsity patterns, etc. The original Fortran-90 code

may contain an arbitrary number of subroutine and function calls, common

blocks, sophisticated solution strategies embedded within the model

evaluation, etc. The information generated automatically by DAEPACK is

exploited in a collection of state-of-the-art numerical algorithms for

performing tasks such as solution of large sets of nonlinear equations,

efficient numerical integration and parametric sensitivity calculation,

hybrid discrete/continuous simulation, and others. In addition, this new

information can be used with third party or custom numerical algorithms to

provide information that would otherwise have to be generated by hand.

Currently, the symbolic components generate:

1) General derivative matrices, J(x)S, where J(x) is the Jacobian matrix

and S is and arbitrary conformable matrix. Setting S equal to the

identity matrix yields the Jacobian matrix. Sparsity is exploited both in

derivative computation and storage.

2) Sparsity patterns.

3) Discontinuity-locked models.

4) Interval extensions of the original system of equations.

In all of the cases above, new code is generated that can be compiled and

linked into other applications to provide the desired information.

Currently, the numerical components provided with DAEPACK are:

1) Block solution of large sparse sets of nonlinear algebraic equations.

The structural information of the system of equations obtained with the

sparsity pattern code described above is used to permute the system into

block lower triangular form where the overall system of equations is

solved as a sequence of smaller blocks. Derivative code is generated in

order to extract efficiently the submatrix of the Jacobian corresponding to

the current block.

2) Efficient numerical integration and parametric sensitivity calculation

exploiting the sparsity pattern and analytical derivatives generated

automatically.

3) Hybrid discrete/continuous numerical integration and parametric sensitivity

calculation using the sparsity pattern, analytical derivatives, and

discontinuity-locked model generated automatically.

4) Intelligent model analysis based on the Dulmage-Mendelsohn

decomposition, exploiting the sparsity pattern generated automatically.

DAEPACK is available on the following platforms: Windows 9x, Windows NT, UNIX

(HPUX and Sun Solaris), and Linux. The Windows versions of DAEPACK are

provided with a graphical user interface that facilitates the automatic

generation of code using the symbolic components.

Future releases of DAEPACK will include a larger set of symbolic and

numeric algorithms and a graphical environment for "numerical

flowsheeting", the construction of numerical algorithms graphically.

Furthermore, greater support for the automatic construction of CAPE-Open

compliant components from legacy Fortran code will be provided.

More information about DAEPACK can be found at the following website:

http://yoric.mit.edu/daepack/daepack.html

For additional information, including licensing, contact:

John Tolsma

Postdoctoral Associate

Department of Chemical Engineering

Massachusetts Institute of Technology

77 Massachusetts Avenue Room 66-365

Cambridge MA 02139

(phone) 617-253-5513

(fax) 617-258-5042

jtolsma@mit.edu

Paul I. Barton

Associate Professor

Department of Chemical Engineering

Massachusetts Institute of Technology, 66-464

77 Massachusetts Avenue

Cambridge MA 02139

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

From: Trini Flores <flores@siam.org>

Date: Fri, 17 Mar 2000 09:10:20 -0500

**Subject: SIAM Annual Meeting**

2000 SIAM Annual Meeting

July 10-14, 2000

Westin Rio Mar Beach Resort and Country Club

Rio Grande, Puerto Rico

LAST CALL!!!

Your contributed abstracts are still welcome! To ensure inclusion in

the Final Program, please send your abstract to SIAM by APRIL 25,

2000.

Don't miss the boat...come, catch the sun!

Even if you don't want to send an abstract, plan to join your SIAM

colleagues for fun in Puerto Rico! Registration materials will be

posted on the web site by March 27.

Visit www.siam.org/meetings/an00/ and submit now your 75-word abstract

in LaTeX format, by using the LaTeX macro available at

www.siam.org/tex/confs/conftex.htm and send it to meetings@siam.org on

or before APRIL 25, 2000.

See you in Puerto Rico!

SIAM Conferences

3600 UCSC

Philadelphia, PA 19104 USA

215-382-9800

800-447-SIAM (US and Canada only)

fax 215-386-7999

meetings@siam.org

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

From: Nick Trefethen <lnt@comlab.ox.ac.uk>

Date: Sat, 18 Mar 2000 16:47:32 GMT

**Subject: Meeting on Pseudospectra of Random Nonhermitian Matrices**

ONE-DAY MEETING ON

(PSEUDO)SPECTRA OF RANDOM NONHERMITIAN MATRICES

Friday, 30 June 2000

Oxford University Computing Laboratory

10.00-5.00

Speakers:

Prof. J. Chalker (Oxford)

Dr. M. Contedini (Oxford)

Prof. E. B. Davies, FRS (KCL)

Dr. M. Embree (Oxford)

Prof. I. Goldsheid (QMW)

Dr. B. A. Khoruzhenko (QMW)

Prof. G. Strang (MIT)

Prof. L. N. Trefethen (Oxford)

For information contact Shirley Day, shirley@comlab.ox.ac.uk

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

From: Yang Xiaoqi <mayangxq@polyu.edu.hk>

Date: Mon, 13 Mar 2000 09:47:05 +0800

**Subject: Sino-Japan Optimization Meeting**

The First Sino-Japan Optimization Meeting

Hong Kong, October 26-28, 2000

The meeting aims to provide a forum for researchers, who are from Japan,

Mainland China, Hong Kong, Taiwan, Singapore, other countries and regions,

and working in the area of optimization, to gather together to report

and exchange their latest works on optimization.

TOPICS INCLUDE

Linear and Nonlinear Optimization

Continuous and Discrete Optimization

Deterministic and Stochastic Optimization

Smooth and Nonsmooth Optimization

Single- and Multi-Objective Optimization

Integer and Combinatorial Optimization

Convex and Nonconvex Optimization

ORGANIZATION AND ENDORSEMENT

The Sino-Japan Optimization Meeting (SJOM) is endorsed by the Mathematical

Programming Society (MPS), the Research Association of Mathematical

Programming (RAMP), Japan, and the Chinese Mathematical Programming Society.

The First Sino-Japan Optimization Meeting (SJOM 2000) is organized

by The City University of Hong Kong and The Hong Kong Polytechnic University.

ORGANIZATION COMMITTEE of SJOM 2000

Liqun Qi (The Hong Kong Polytechnic University), Co-Chair

Jianzhong Zhang (City University of Hong Kong), Co-Chair

Chuangyin Dang (City University of Hong Kong),

Xiaoqi Yang (The Hong Kong Polytechnic University), Treasurer

GUEST PLENARY SPEAKERS

Rainer Burkard (Technische Universitat Graz, Austria)

Gianni Di Pillo (Universita di Roma ``La Sapienza'', Italy)

Carl Timothy Kelley (North Carolina State University, USA)

Jean-Philippe Vial (University of Geneva, Switzerland)

FURTHER INFORMATION

e-mail: Eva Yiu (maevayiu@polyu.edu.hk) or Peggy Chan (machan@cityu.edu.hk)

webpage: http://www.polyu.edu.hk/$\sim$ama~

or contact Organization Committee Members

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

From: George Miminis <george@cs.mun.ca>

Date: Sun, 12 Mar 2000 18:26:43 +0200

**Subject: Department Head Position at Memorial University**

MEMORIAL UNIVERSITY OF NEWFOUNDLAND

HEAD OF COMPUTER SCIENCE

Applications and nominations are invited for the position of Head of the

Department of Computer Science. The starting date is negotiable.

Memorial University is the largest university in Atlantic Canada. As

the province=92s only university, Memorial plays an integral role in the

educational and cultural life of Newfoundland and Labrador. Offering

diverse undergraduate and graduate programs to almost 16,000 students,

Memorial provides a distinctive, and stimulating environment for

learning. St. John=92s is a very safe, friendly city with great historic

charm, a vibrant cultural life, and easy access to a wide range of

outdoor activities. The Department of Computer Science has 20 faculty

and 13 technical and support staff, offers a full range of undergraduate

and graduate programmes and is a critical component of an

interdisciplinary computational sciences (graduate) programme.

The ideal candidate for head will have a strong record of research and

teaching in computer science or related area, demonstrated

administrative skills, a commitment to collegial

governance, interests that span all aspects of information technology

and a desire to create links with industry and other academic units on

campus. Applications or nominations, which include a Curriculum Vitae

and the names of at least three potential referees should be sent to Dr.

Edgar G. Goodaire, Chair, Search Committee for Head of Computer

Science, Office of the Dean of Science, Memorial University of

Newfoundland, St. John's, Newfoundland, Canada, A1B 3X7. Applications

received by June 30, 2000 will be assured consideration.

In accordance with Canadian Immigration requirements, this advertisement

is directed towards Canadian citizens and permanent residents of

Canada. Memorial University of Newfoundland is committed to employment

equity. Memorial University is part of a vibrant, local scientific and

engineering community which maintains an inventory of available

positions for qualified partners. Partners of candidates for positions

are invited to include their r=E9sum=E9 for possible matching with other job

opportunities.

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

From: Gustaf Soderlind <gustaf@maths.lth.se>

Date: Mon, 13 Mar 2000 12:00:00 +0100 (MET)

**Subject: Faculty Position at Lund Institute of Technology**

Lund Institute of Technology in Lund, Sweden, has an open

position as full professor of scientific computing. We seek

applicants having a strong record in constructing, analyzing,

developing and applying new numerical methods and mathematical

models in computational problems of importance in science and

engineering. Further information about the position is available

at the web-site

www2.lth.se/ledjobb/prof/index_e.asp

Applications are due April 19, 2000.

Gustaf Soderlind

Numerical Analysis

Center for Mathematical Sciences

Lund Univeristy

Box 118

SE-221 00 Lund, Sweden

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

From: Reneaume Jean-Michel <jean-michel.reneaume@univ-pau.fr>

Date: Mon, 13 Mar 2000 09:24:42 -0000

**Subject: Postdoctoral Position at ENSGTI, Pau, France**

Within the SIMAPI (SIMulateur Aquitain de Procedes d'Incineration) project,

the LGPP (Laboratoire de Genie des Procedes de Pau) establishes physical

models describing incineration processes. As a background, a steady state

model for fluidised bed incinerator has been developed. The objective of

this postdoctoral position is to complete the existing model in order to

allow dynamic simulations :

* Transition from steady states.

* Start up of the process.

* Incidents on the process.

Working conditions as well as environmental impact are the two governing

variables that need to be simulated.

The LGPP has a position for one postdoc during 12 months. The beginning of

the position is planed for July 1st 2000. This laboratory is looking for a

highly-qualified researcher with a great autonomy, having background in

Chemical Engineering, process modelling, numerical methods, simulation

systems and programming.

Inquiries should be directed to Jean Michel Reneaume. Email or write with

full CV and contact details.

Jean Michel Reneaume

LGPP-ENSGTI

Rue Jules Ferry

64000 Pau France

Tel: 33 - 5 59 72 20 47

Fax: 33 - 5 59 72 20 81

Email: jean-michel.reneaume@univ-pau.fr

URL: http://www.univ-pau.fr/ser/CURS/LGPP/accueil.html

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

From: Alfio Quarteroni <alfio.quarteroni@epfl.ch>

Date: Thu, 16 Mar 2000 11:14:14 +0100

**Subject: PhD Position at EPFL**

Ph.D Position at Ecole Polytechnique Federale de Lausanne

The Ecole Polytechnique Federale de Lausanne (Switzerland) is seeking

a qualified candidate for a Ph.D position funded by Swiss National

Science Foundation (FNS). The project will be coordinated by

Fluid Mechanics Laboratory Department of Mechanical

Engineering & Department of Mathematics.

The title of the proposed programme of research is

"Spectral Element Methods for Viscoelastic Flow Problems". Suitable

applicants should be qualified mathematician or engineer.

Further information about the EPF Lausanne may be found on its

web page http://www.epfl.ch. The successful candidate will join a

thriving research-oriented Department and have access to a wide

variety of computing platforms for the duration of the project

(at least three years.)

Applications in the form of a covering letter, a full C.V. and the

contact details of three referees may be posted, faxed or emailed

(by April 15) to

Prof. Robert G.Owens,

DGM-IMHEF-LMF, EPFL,

CH-1015 Lausanne, Switzerland

Tel: ++41 21 693 3589

Fax: ++41 21 693 36 46

Email: Robert.Owens@epfl.ch

http://imhefwww.epfl.ch/lmf/staff/owens/advert2.html

or to

Prof. Alfio Quarteroni,

DMA, EPFL,

CH-1015 Lausanne, Switzerland

Tel: ++41 21 693 5546

Fax: ++41 21 693 4303

Email: Alfio.Quarteroni@epfl.ch

http://dmawww.epfl.ch/Quarteroni-Chaire/index.html

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

From: Roland masson <roland.masson@ifp.fr>

Date: Thu, 16 Mar 2000 13:32:11 +0100

**Subject: PhD Position at Institut Francais du Petrole, Paris**

We have grants from the EC HUMAN program, for supporting European

researchers (PhDs and post-docs) in our department, in association with

our subsidiary BEICIP-FRANLAB. These grants are available now. In

particular we propose the following PhD position in scientific computing:

PHD FELLOWSHIP IN SCIENTIFIC COMPUTING

Domain decomposition methods for modelling hydrocarbon reservoir formation

Basin modelling aims at reconstructing the time evolution of a sedimentary

basin in order to make quantitative predictions of geological phenomena

leading to oil accumulations. It accounts for porous medium compaction,

hydrocarbon formation and migration.

Recent evolutions of basin simulators have contributed to improve

the treatment of geological discontinuities such as faults. These faults

divide the basin into blocks whose deformations cause geological layers to

slide between themselves. A natural discretization of these complex geometries

involves sliding meshes which do not match.

The goal of this PHD is to propose, to analyse and to implement adequate

numerical methods. The domain decomposition approach will be used as it enables

efficient handling of non-matching grids. Moreover, it is well suited to

parallel computing.

The candidate will join the scientific computing group of the Computer

Sciences and Applied Mathematics Department of IFP. He will work within the

basin modelling and reservoir simulation projects. Applicants should posess

some background in numerical simulation of PDE's and linear algebra as well

as programming experience in C.

To apply, send a CV and references to

Isabelle Faille, Computer Sciences and Applied Mathematics Department,

IFP, e-mail: isabelle.faille@ifp.fr or

to Frederic Nataf CMAPX, Ecole Polytechnique, Paris, e-mail:

nataf@cmapx.polytechnique.fr

Roland MASSON

Institut Francais du Petrole

1 et 4 av. de Bois-Preau, BP 311

92852 Rueil-Malmaison Cedex tel : +33 1 47 52 71 33

FRANCE fax : +33 1 47 52 70 22

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

From: Vaibhav Deshpande <vaibhav@cscs.ch>

Date: Thu, 16 Mar 2000 10:38:58 +0100

**Subject: Visiting Positions at Swiss Center for Scientific Computing**

Call for Participation in VISITING RESEARCHER PROGRAM (VRP 2000) at CSCS

As part of its educational initiative, the Swiss Center for Scientific

Computing (CSCS) has traditionally conducted two separate student

programs (SSIP and PRSS) which offered a unique opportunity to students

from within Switzerland and abroad to work on specific projects during

their stay at CSCS. From this year onwards, CSCS will organize

Visiting Researcher Program (VRP 2000). This new program, which

supersedes the two separate programs, offers additional possibilities

to not only young students but also junior and senior researchers

active in their field to broaden their horizons of knowledge and gain

unique experience during their stay at CSCS.

While interacting with experts within and outside of CSCS, invited

candidates will either carry out a project proposed by CSCS or will

have the freedom to define and conduct their own project which will be

relevant for CSCS. Topics include, but are not limited to, problems in

computational modeling, computer graphics and visualization, software

engineering and information processing.

The program will commence in July 2000 with a period of stay from a

few weeks to a maximum of 4 months. Candidates are strongly

encouraged to seek funding from indigenous sources. For those without

adequate funding, CSCS may pay a fixed stipend (up to CHF 2200

max. per month) to cover the stay and travel expenses.

The program is open to Swiss and foreign postgraduate students and

researchers with background and research interests in Computational

and/or Computer Sciences and Engineering. Undergraduate students of

exceptional merit who intend to pursue higher education in these areas

may also apply. Applications will be screened to invite a limited

number of candidates.

More details about the program and the application procedure can be

found at CSCS web site (http://www.cscs.ch/education/edu_vrp.html or by

email to VRP2000@cscs.ch). The closing date is 31 March 2000 for

international applications and 30 Apr 2000 for Swiss applicants.

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

End of NA Digest

**************************

-------