Numerical Analysis

Archive for February, 2010

?Numerical Recipes? SAVGOL

Hello, everyone,

       Can anyone please help me use subroutine SAVGOL correctly,
in order to get the derivatives of a data set?
       The book(Numerical Recipes in Fortran) says SAVGOL gives
convolution coefficients for smoothing or derivatives, according
to the value of variable ld, which is 0 for smoothing and N for
Nth derivative.
       I had no problem to smooth a data set with SAVGOL, but
when I tried to get the first derivative of a noise-corrupted
sine wave function(just for test), I couldn’t get a cosine
until I decreased m, the order of smoothing polynomial, down to
2, and the window down to 3 points long, which according to the
authors are not recommended for derivatives.
(I can’t even make it work on a perfect slow sine waveform.)

       Any advice will be appreciated.  
       Thanks in advance.

Jianhong Wang
Univ. of Guelph
Ontario, Canada

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Bispectral Data Analysis

I am seeking algorithm implemetations of both the direct
and indirect methods.  I am also interested in test data
for evaluating the operation of the algorithms with known
results or of algorithms for data generation with known

Please E-Mail with answers or questions.

Thank You
David …

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surface interpolation? ie, f(x',y') <<– [x,y,x',y',f(x,y)]

Hi, Like the header says I’d

I’d like to interpolate some 3D data (a function of two variables).
Can anyone recommend a source ?

Ira Ekhaus

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Solutions to chaotic Euler-Lagrange BVP's via direct methods: Explain?

Fermat’s principle in optics (and acousitcs) states that optical rays are  
paths for which the travel time integral is a local minimum wrt to  
perturbations in the paths. In 2-D problems for which the speed of  
propagation in the medium varies with both coordinates, the differential  
equations  for the rays produce chaotic solutions. These ODE’s are the  
Euler-Lagrange equations of the travel time integral.

If the problem of tracing rays is treated as a boundary value problem, and  
if the travel time integral is attacked using so-called ‘direct methods’  
(e.g. Rayleigh-Ritz, or a Monte Carlo method such as simulated annealing),  
solutions can be obtained in cases where initial value (‘shooting’)  
techniques fail miserably. In particular, we have studied propagation  
speed  c(r,z) = c0(1 + a * cos(kr*r) * cos (kz*z)) where a=0.02, c0=1.5,  
kz=2*pi/0.5 and kr=2*pi/20. Travel time integral is
T=int( sqrt( 1+(dz/dr)^2)/c(r,z)*dr) from r0 to rf.

[Jour. Acous. Soc of America will have an article by Collins and Kuperman,  
probably in June, on this phenomenon. I have also submitted a paper to  
same journal, K. E. Gilbert co-author.] I would appreciate any response  
which can explain or shed light (sorry for the pun) on this phenomenon. I  
can provide more detailed background on the problem and our work to  
interested respondents.

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help on Electical Impedance Tomography with FEM

I am working on solving the following problem. An inhomogenous
resistiviy medium is surrounded with some electrodes into
which are injected some static currents. The voltage medium
response is recorded through other boundary electrodes.

The direct problem consists in dertermining the voltage distribution
from the knowledge of the current distribution and the resistivity
distribution. I am trying to solve this with the finite element
method, but I have no special bibliography on this particular appplication,
especially with static currents. Could anyone provide me with bibliography
on that matter, especially about convvergence rate ? Does there exist any
means to measure the precision of the FEM solution with respect to the
size of the elements ?

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Outer-Approximation for MINLP

I am currently attempting to solve a Mixed Integer Nonlinear Programming
(MINLP) problem using the ‘Outer-Approximation’ algorithm as described in

Viswanathan, J. and Grossman, I.E. "A Combined Penalty Function and Outer-
Approximation Method for MINLP Optimization," Computers Chem Engng, Vol. 14,
No. 7, pp769-782, 1990.

I would be interested in hearing from anybody who has had any experience in
implementing this algorithm.  In particular, the problem I am solving has
a tendency to generate infeasible NLP subproblems.  Following the advice in
the reference, I have reformulated the problem to incorporate a ‘relaxation’
variable, but it is not clear how to treat the relaxation variable in the
MILP (i.e. should it be included there also?).  I would also appreciate
any advice on the following:

1) Are there any more recent references to this algorithm?

2) Are there any other newsgroups I could subscribe to which might offer
   some useful info?

3) Does anyone know Ignacio Grossman’s email address/whether he would mind
   being contacted directly?

4) Are there any other algorithms for MINLP (other than nonlinear Branch &

Thanks in advance,

Ian Boyd

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Hi num-analysts

I am interested in the simulation of differential algebraic (implicit)
equations (DAE).

I understand that the calculation cost can be reduced if irreducible blocks
of algebraic equations are teared to break the algebraic loops. It can be
seen as removing of vertices in the (undirected) graph of equations and
variables to remove all strong components (in the directed graph which
we get when equations are matched with variables).

As I understand the minimum set of tear vertices can not be found in
polynomial time. Consequently several heuristics can be applied. I have found
some good articles about tearing e.g.:

1) "implicit enumeration" algorithm described in
R.W.H. Sargent "The decomposition of systems of procedures and algebraic
equations" in Numerical Analysis, lecture Notes..G.A Watson 1978

2) M. Shacham "Decomposition of systems of nonlinear algebraic equations"
AiChE Journal (vol.30,n.1) 1984

My questions are:

1) Is anybody of you experienced, interested in the subject of tearing ?
Do you want communicate in this subject ?

2) Could you please send me some pointers to other good, more recent texts,
articles on tearing.

3) Are you aware of any running implementation of some tearing algorithm ?

Any hint is welcome. Send e-mail to me and I will post a summary to this
newsgroup. Thanks for responses.

Pawel Bujakiewicz
TU Delft, Control Lab. 5031 2600 GA Delft, The Netherlands
tel: 31+15-785591  fax: 31+15-626738
email: pawe…

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approximations for sine and cosine functions

Does anybody know where I can get some good information on computing
the approximations for the sine and cosine functions and thier
associated errors.
My name is Mark Hawkins.  Please send any information to me at

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Simplex method and its computational complexity (repost)

In "Numerical Recipies in C", it says that the simplex method is first
published by Dantzig in 1948 but it is not proved until 1982 that the
algorithm will take O(max(M,N)) time. I couldn’t find where this result
is first published, so if you know any references or pointers to references
about this result, please reply by e-mail. Thanks …

O. Toker

E-address = tok…

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4postdoc in Biomathematics seeking a Research position.

Greetings, everyone!
I am a researcher in Biomathematics at the Institut de Biologie Theorique,
Universite d’Angers, France. I am seeking for a position in Mathematics or
 in Applied Mathematics, in the domain of neural network or mathematical
modeling in intestin phenomena. I am ready  to  do  researches  in other
areas of biomedical research.

I have B.Sc. in Pure Mathematics and Physics, I have 2 Ph.Ds. in Applied
Mathematics and Physics.
I had  worked  one  year  as a  postdoc  fellowship in school of medicine,
University of Nevada, Reno.

So, I can teach mathematical and physical courses for undergraduates too,
I have five years experience in this domain.

Thanking you in advance for the help you could give me,

   Dr. Sameh Metry
   Institut de Biologie Theorique
   Universite d’Angers
   10, ru Andre Boquel
   49100 ANGERS
   Tel. : 41 72 34 45
   Fax. : 41 72 34 46
   E.mail: me…

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