Numerical Analysis

Archive for March, 2010

Not-diagonally-dominant matrix, iterative solution of

Hello everyone,

I have a question regarding the sparse matrix solver which I have
discussed with a friend of mine.

     AX=0 (an eigenvalue problem)

where, the matrix A is from the standard five-points finite-difference
discretization. It is sparse banded matrix with only five non-zero
each row. It is looks like:

     1/dy/dy……..1/dx/dx -2/dx/dx-2/dy/dy+K  1/dx/dx……..1/dy/dy

where dx, dy are the mesh size in X- and Y-dimension.

In the discussion, if the parameter K<0 (valid for most grids),
then A matrix is diagonal dominant, and the sparse matrix solver,
such ORTHOMIN, BI-CG, or BI-CGstab may be used.

The problem is, at some grids, the K>0, which destroys the diagonal
dominance. In this case, will the sparse matrix solver converge ?
BTW, the preconditioner used is DKR factorization.

Thanks in for any suggestion.

Fred

.
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Optimization question, and Method for sample picking ?

Given N absorption spectrums ( # of samples) of dimension M,

 A(i,j) = alpha(i) * concentration(j) * path + scatter(j)

My objective is to find alpha(i), i=1,…,M
A(i,j) known and measured
concentration(j),scatter(j) are scalars for each spectrum but are not known

QUESTION :
   -What is the best method to pick the best data and remove any outliers ?

   - Is Nonlinear optimization the only way to find alpha(i), by finding
     alpha(i),con(j) and scatter(j)  i=1,…,M   j =1,…N

Regards
Saad J Bedros

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Professorship in applied analysis

The Swiss Federal Institute of Technology in Lausanne, Switzerland (alias EPFL
= Ecole Polytechnique Federale de Lausanne) invites applications for a

          Faculty position in Applied Analysis

The teaching duties will include mathematics courses for engineering students,
as well as courses for students in mathematics. Willingness and talent to teach
at all university levels is a requirement.

The new professor is expected to lead an important research activity in areas
of applied analysis. In her/his research, the new professor is expected to
collaborate actively with existing research groups at EPFL.

Applicants should have shown ability to carry out and to direct high level
research projects.

Female applicants are particularly welcome.

Deadline for applications: 31 October, 1994.

Start of appointment: as convenient.

For more information concerning this position, interested persons can write to
   EPFL, Office of the President, CE-Ecublens, CH-1015 Lausanne
and/or e-mail to
     bur…@pres.adm.epfl.ch  (Mr Marius Burgat)
or   silv…@pres.adm.epfl.ch  (Mrs Jeannine Silvant)

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Help with Pade-Approximation, please!

Dear netresses & netters,

I am just about to finish my thesis in theoretical Chemistry involving
the numerical Pade approximation of potentials. Now I am faced with the
following problem:

I’m fitting rational functions to data points (Pade kind) trying to minimize
the least squares error on the polynomial

                            2      3                
            a0 + a1*x + a2*x + a3*x + …

Pn,m(x) = ————————————
                                2      3    
            1 + b0 + b1*x + b2*x + b3*x + ….

How can I determine the coefficients by minimizing the least squares
problem under the condition that the denominator has no roots in the
interval [Xmin, Xmax], i.e, does not become singular?

Thanks very much in advance for any help or pointers,

PS: Please make any answers via email and I’ll summarize if
there’s general interest.

Oliver.


Uwe ‘hoover’ Schuerkamp                   hoo…@mathematik.uni-bielefeld.de
University of Bielefeld, Germany                     Phone: +49-521-106-3871

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Textbook Wanted

Textbook Wanted:

Advanced Calculus for Applications, 2nd edition (1971) by Hildebrand.

[Preferably without any highlighting or underlining.]

If you have a copy of this book that you are willing to sell, please send
email to:  rkban…@eos.ncsu.edu

PLEASE DO NOT REPLY TO THIS ACCOUNT, as I am posting this article for a
friend.

Thanks!

P.S. – I apologize if I have posted this article to an irrelevant newsgroup.

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Discrete Time Simulators in C++

Dear Netters,

        Does anyone out there have any experience
using/writing/designing discrete-time simulators in C++.  My problem
involves a large-scale transportation network with dynamic-stochastic
arc costs, and I would like to model it using a discrete-time simulator
mixed in with a bit of optimization.  Any advice, references or code samples
would be much appreciated.

Thanks,

Joel Shapiro
Princeton University

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C/C++ source/help for logistic curve fitting

Hi…

        Could anyone help me with formulation of logistic constants.  I am
        looking for info on how to approach summing in the context of a C++
        program.

        In case you are interested, it is for the modelling of a bio-
        leaching scenario for my chem engineering undergrad thesis.  (I’m
        not an ultra-hot mathematician)…

        Thanks a lot… (in advance…)
                0 0
                 "
                \_/   tee hee

Cheers

Shrapnel

Karen van der Linde
vlnka…@chemeng.uct.ac.za

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FUZZY- LINEAR OR FUZZY GOAL PROGRAMMING ALGORITHMS

 Is there any code for solving multiple objective linear programming?
 My work is further complicated by the fact that my model parameters
 and coefficients are fuzzy. How can I treat this aspect in linear or
 goal programming model? Sequential solving of the objectives is so
 far the way I envisage solving the goal problem but only in its crisp
 format. You help will be most appreciated: comments and suggestions too
  _______________ Thanks in advance _______________
                     chabva

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Time Marching Method

Is there anyone out there who can point me in the direction of any information
on time marching methods for blade to blade flows.  I am particularly
interested in the work of J. Denton.  I would like as much information as is
possible on the stability of these methods and the boundary conditions in
particular.

I would appreciate any suggestions of journals, books, etc. where I can get
this information.  Any anonymous ftp sites which contain time marching
information or source code would be wonderfull.

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looking for vectorized random number generator

Hello,

I am poking around for a vectorized random number generator, and was
wondering if anyone has one.  

The "dmod" function was not listed as a vector function in any of my
3090 or Cray manuals, so I am wondering if it isn’t vectorizable.  

It would be great if someone has vectorized the LAPACK random number
generator.  

Sincerely,
Tim

Tim Burns                               email: t…@osiris.usi.utah.edu
USI, 85 SSB, Univ. of Utah, UT  84112   phone: (801)581-5172
+————————————————————————–+
| Great Salt Lake:  wilderness adjacent to a city; a shifting shoreline    |
| that plays havoc with highways; islands too stark, too remote to inhabit;|
| water in the desert that no one can drink.  It is the liquid lie of the  |
| West.                                                                    |
+————————–            –Terry Tempest Williams ———–+

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