Newsgroup sci.math.num-analysis 29174

Directory

Eventus company wrote:
> 
> How to do this or where to find a software? Non-zeros are distributed
> uniformly over the matrix, without any pattern.
Hi,
there are not only these books, but here is actual software. Check out
netlib,
www.netlib.org. Look in directories laso, lanz etc.
-- 
Hans D. Mittelmann			http://plato.la.asu.edu/
Arizona State University		Phone: (602) 965-6595
Department of Mathematics		Fax:   (602) 965-0461
Tempe, AZ 85287-1804			email: mittelmann@asu.edu

I've been working with fourier transforms to evaluate optical systems.
Up until now I was quite happy with a relatively simple 2 dimensional
approach; A narrow slit is projected by the system i'm examining on a
CCD camera. I know the stimulus, I measure the response signal on the
camera.
The math is done on a PC, using LabView from national instruments.
LabView has a lot of standard functions, witch include fourier
transforms.
But now I've got a problem at hand that should be solved in a different
way: I need a 3 dimensional fourier transform.
I've been looking for a descripion of the math involved in a 3D FFT,
with no success till now.
Note: I'm not keen on writing an algorithm from the bottum up, I would
very much like a solution that fits in my LabView enviroment, speed is
of secondary interrest.
Anyone with a solution?

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In article <32AED745.6CFA@ese-metz.fr>,
Delphine Wolfersberger   wrote:
>I have got a problem to solve a partial differential equation using 
>the Galerkin method. At the end of the calculation, I obtain a system 
>of differential equations that is not solvable. What can I do? 
You had better explain just what you mean by "not solvable".

Hi to all,
just to refresh my old calculus course: given the infinite sum of
(1-a)^m (a<1), what can I say about ? More precisely:
For a<1 the does the sum converges ?
What is the limit (as a function of a, of course) ? 
The condition a<1 is necessary or sufficient (or both) for the
convergence ?
Any suggestion will be very appreciated
Best regards
 vanni guarnieri

Hi everybody!
I am looking for freeware subroutines for computing the 
inverse of a large sparse matrix. Is there anybody who knows 
the fastest way for getting them? 
Thanks in advance for your precious help.
Agostino

Hi,
What is the best way to evaluate (double precision IEEE compliant)
sqrt(1-x*x) when x -> 0 ?  
Currently I am using: 
sin( acos( x ) ) 
Which can be trusted if acos() and sin() are evaluated accurately?
What can one expect when using:
sqrt(1+x) * sqrt(1-x)
Using 1-x*x is of course not an option.
How does MATLAB handle this?
>> sin(acos(1.0e-8))
ans =
     1
Thanks in advance.
Best Regards.
Serge
-- 
	     Short Course on Domain Decomposition Methods
	       http://www.cs.kuleuven.ac.be/~serge/dd/
--
     Serge.Goossens@cs.kuleuven.ac.be        Department of Computer Science
     http://www.cs.kuleuven.ac.be/~serge/    Katholieke Universiteit Leuven
     Phone: +32 (0)16 327087                 Celestijnenlaan 200A
     Fax:   +32 (0)16 327996                 B-3001 Heverlee        BELGIUM

In article ,
Serge Goossens   wrote:
>Hi,
>
>What is the best way to evaluate (double precision IEEE compliant)
>sqrt(1-x*x) when x -> 0 ?  
As soon as x is sufficiently small (i.e. smaller than about 1e-8)
you can simply use 1.
Besides being very fast is it also the correct answer rounded to
double precision IEEE.
The important part is that you should not use expressions like
sqrt(1-x*x)-1, because then you get cancellation NO MATTER HOW
you compute sqrt(1-x*x).
Since the values of sqrt(1-x*x) for x->0 only differs by roundoff errors 
I see no reason to prefer one form in favour of another one.
--
// Homepage  http://www.dna.lth.se/home/Hans_Olsson/
// Email To..Hans.Olsson@dna.lth.se [Please no junk e-mail]

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