Newsgroup sci.math.num-analysis 29214

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: >There is a book on the history of Pi by Petr Bekkman (or some spelling
: >like
: >that).  Check it out.
A History of Pi by Petr Beckmann.  St Martin's Press, New York.
-chris.

Grant Hiebert wrote:
> 
> I have been able to find many examples of algorithms that generate cubic
> splines for (x,y) series of data, but they all insist that the "x" series be
> layed out as such x(1) < x(2) < x(3) < x(4)...... x(n-1) < x(n).
> 
> Does anyone know of one that allows for values of "x" that do not follow this
> pattern (ie. the spline doubles back over itself)?
Just parameterise your curve differently. Use 2 splines
x(t) and y(t) to describe your curve {x(t),y(t)}, where t is a "good"
partition of the interval, for instance 1,2,3,4,5...

I have made a simple Win 95 program that simulates the movements of bodies in 
space, subject only to the force of gravity. It works in discrete steps, first 
it computes the accelerations of all bodies and changes their speeds 
accordingly (acceleration due to the gravity of all other bodies) then all 
bodies are moved according to their current speed. These two steps are 
repeated over and over again,making the objects move.
Now, as long as the objects are far apart this works perfectly. The problem 
appears when a small object comes close to a large one. The smaller object is 
then sometimes flung out into space. I can circumvent this problem by making 
gravity stop working at distances below a certain point. This however only 
eases the problem, and does not solve it. Whatever I do I cannot with this 
current model keep the potential + kinetic energy of objects passing near 
large objects constant.
The reason for the problem is this: say the object passes the sun in three 
steps, like this:
	    1			         2			3
	    o				.o			o	.
	.  
In this case the object receives an enormous acceleration in step 2 that is 
never correctly compensated for.
How do you suggest I solve this problem? As I see it the whole 
discrete-step-approach is useless, and I'll have to rewrite the whole 
simulation engine. Does anyone know of any other possible approach?
--Lars M.
______________________________________________________________________________
______

robin (rav@goanna.cs.rmit.edu.au) wrote:
: Daniel Zagar  writes:
: 	>I am writing a serial interface and i need the exact information about
: 	>representation of floating point numbers, ie bit patterns etc.
: 	>  What is the standard on Windows NT?
: The standard doesn't depend on the operating; the standard depends on
: the computer hardware you are using.
: Therefore, you need to get a manual for the particular hardware.
: For an Intel machine, you need the hardware manual for the x86,
: for example.
: 	>  What is the standard on IRIX?
: 	>Information about reference manuals with IEEE or corresponding standard
: 	>numbers or is also needed.
I think, the standard depends on the CPU too, but if you use the IEEE
standard, you normally will do nothing wrong, also Intel machines (the FPU)
can use the IEEE standard. 
In every book dealing with floating point operations you should find the
requested answers about the IEEE standard. Why do you want to use floating
point numbers ?
Andre

  I'm trying to use a superquadric to interpolate 3D points, I tried the 
approach proposed by R.Bajcsy and F.Solina but i can't understand how they 
programmed their minimisation of their 11 parameters ( 3 rotation 3 
translation 5 superquadric parameters), they use a non linear minimization 
using least square method but the thing to minize is so hudge that i really 
don't know how they programmed it
I hope someone can help me 
Best regards
R.Blume
contact at rbo@robo.jussieu.fr

I have a matrix P that contains known x,y,z (coordiantes of 3D points)
      x.............
P=  y .......
      z .......
      1 .........
I apply to these points a rotation and translation matrix R, matrix R contains 
is function of the 3 euler angles and 3 translation.
thenew 3D points that i ll get by multiplying P by R must fulfill the 
following equation where a1 a2 a3 e1 e2 are parameters to determine
(((x/a1)^(2/e2)+(y/a2)^(2/e2))^(e2/e1) +(z/a3))^(e1/2)=1
Knowing the initial points x y s  i want to minimize the expression to 
determine a1 a2 a3 e1 e2 but also the rotation matrix angles and translation 
parameters.
The minimization is so hudge that i can't program it even if mathematicaly 
everything works if anyone can help me i 'll be grateful
thanks
please contact me via email: rbo@robo.jussieu.fr

On 16 Dec 1996, Lars Marius Garshol wrote:
> 
> I have made a simple Win 95 program that simulates the movements of bodies in 
> space, subject only to the force of gravity. It works in discrete steps, first 
> it computes the accelerations of all bodies and changes their speeds 
> accordingly (acceleration due to the gravity of all other bodies) then all 
> bodies are moved according to their current speed. These two steps are 
> repeated over and over again,making the objects move.
> 
> Now, as long as the objects are far apart this works perfectly. The problem 
> appears when a small object comes close to a large one. The smaller object is 
> then sometimes flung out into space. I can circumvent this problem by making 
> gravity stop working at distances below a certain point. This however only 
> eases the problem, and does not solve it. Whatever I do I cannot with this 
> current model keep the potential + kinetic energy of objects passing near 
> large objects constant.
> 
> The reason for the problem is this: say the object passes the sun in three 
> steps, like this:
> 
> 
> 	    1			         2			3
> 
> 	    o				.o			o	.
> 
> 	.  
> 
> In this case the object receives an enormous acceleration in step 2 that is 
> never correctly compensated for.
> 
> How do you suggest I solve this problem? As I see it the whole 
> discrete-step-approach is useless, and I'll have to rewrite the whole 
> simulation engine. Does anyone know of any other possible approach?
> 
> --Lars M.
> 
What you essentially need to do is to solve the set of differential 
equations describing the motion of each body. Your present approach 
sounds like the simplest method to do so, the so-called Euler Step. This 
method is usually not sufficient.
The problem you describe is usually solved by "adaptive stepsize control".
A good method to solve this kind of problem are so-called "embedded
Runge-Kutta Formulae" (some well known variants are called
Runge-Kutta-Fehlberg.) Another variety which may be useful here is called
Runge-Kutta-Nystrom (for second order diff. equn's without first
derivatives). 
If you have trouble finding references for these, I can tell you some 
literature pointers.
Good Luck,
Gerhard
=====================================================================
  Gerhard Heinzel                          E-mail:   ghh@mpq.mpg.de
  Max-Planck-Institut fuer Quantenoptik
  Hans-Kopfermann-Str. 1                    Phone: +49(89)32905-268
  D-85748 Garching                                             -252
  Germany                                     Fax: +49(89)32905-200
=====================================================================

In article , 
ghh@mpq.mpg.de says...
>
>The problem you describe is usually solved by "adaptive stepsize control".
>A good method to solve this kind of problem are so-called "embedded
>Runge-Kutta Formulae" (some well known variants are called
>Runge-Kutta-Fehlberg.) Another variety which may be useful here is called
>Runge-Kutta-Nystrom (for second order diff. equn's without first
>derivatives). 
>
>If you have trouble finding references for these, I can tell you some 
>literature pointers.
I do have trobule, so yes, please, I'd like to have as many pointers as possible. Do you know of 
any online sites that carry this kind of information?
Thanks,
--Lars M.

I want to calculate the derivative of a digitized signal using
a numerical filter/algorithm.  A straight finite difference
technique amplifies the high frequency noise.  The signal is
not sinusodial and would need many terms in a fourier series
to approximate it.  I want to accurately determine the
low frequency derivative.  Is there a reference book that
addresses this?  Is there a suggested smoothing->finite derivative->
smoothing algorithm for doing this?
thanks,
mike
-- 
	Michael John Bergmann	919-660-2547	(home) 956-8439
	Dept. of Physics box 90305, Duke University
	Durham, NC 27708-0305    http://www.phy.duke.edu/~mjb

In <593rm7$3nh$1@o.online.no> larsmg@online.no (Lars Marius Garshol) writes:
> 
> I do have trobule, so yes, please, I'd like to have as many pointers as possible. Do you know of 
> any online sites that carry this kind of information?
Take a look at the FAQ for this group.  It has a whole section on the
n-body problem.  Doing a web search on the "n-body problem" will also
give you a lot of pointers, including pointers to various programs.
The n-body problem is a fun thing to work on.  There are lots of
programs and stuff out there on it.  I also have written a program
called "Xstar", which you might be able to find by doing a ftp
search.  If you are interested, I can send you a copy of the latest
version, which includes a rather large report on the subject.  (About
600k total)
-wayne
-- 
Wayne Schlitt can not assert the truth of all statements in this
article and still be consistent.

Hello,
I have found a paper describing an interesting method for protein sequence
analysis (CABIOS vol.6 no.2 1990 pp71-80), but couldn`t understand the
following:
transpose -of 1 or 2 dim. matrix
unitary vector
eigenvector
Anyone willing to explain these to a biologist, please?
If so, contact me by e-mail.
Fragments of the paper:
...Then the power spectrum Ps(v) of h may be written: [ ] where nt is the
transpose of n. ...
...where Ws(v) is a non-negative definite symmetrical matrix. Thus, the
unitary vector n0 which maximizes Ps(v) is the eigenvector of Ws(v)
associated with the largest eigenvalue l0(lambda zero).
Thanks,
##rozkwas zasady##
Piotr Muszynski
u0295020@msv.cc.iwate-u.ac.jp
Kamido 3-12-30-F, Morioka
020 Iwate, Japan

Hi Lars,
I guess you have just discovered the slingshot effect, which can be
used when travelling in space. As I understand, the attractive
gravity forces pulls the bodies together, and, if then their
relative velocity becomes larger than the escape velocity, the
bodies are swung apart with high speed.
So if you think your results are unphysical, don't worry! It's
reality!
However it's important to use a short timestep if the velocity is
high. You have to follow the paths closely to get a good result.
You ask if the discrete-step-approach i useless, and I would
definitely say no, because discretization is what computational
math is about (almost!). Personally, I would solve your problem by writing
down the continous differential equations and then use some
ready-made program/package to solve it. For example ODEPACK in FORTRAN
or Matlab (recommended!). These methods usually are very efficient
and varies the timestep depending of the equation.
Mattias

                     C A L L   F O R    P A P E R S
            Special Session on Parallel Stochastic Optimization
                  1997 Parallel and Distributed Processing
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                        Las Vegas, Nevada
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The extended abstracts (4-5 pages, double-spaced) should be sent to 
G. S. Stiles, Electrical and Computer Engineering, Utah State University, 
Logan, Utah, 84322-4120, by February 12, 1997.  E-mail submissions 
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The first page of the abstract should include: title of the
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-- 
--------------------------------------------------------------------------------
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Real-Time and Parallel Computing Group   http://multi.ece.usu.edu
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michael j bergmann wrote:
> 
> I want to calculate the derivative of a digitized signal using
> a numerical filter/algorithm.  
stuff deleted ...
I used the Savitzky-Golay filters for that.  Check them out in the
second edition of Numerical Recipes.
-- 
Mirko Vukovic, Ph.D   	3075 Hansen Way M/S K-109
Varian Associates	Palo Alto, CA, 94304
415/424-4969		mirko.vukovic@varian.grc.com

R&D; Engineer (Multi-phase Porous Media Flow)
--------------------------------------------
Position at COMCO, Austin, TX
------------------------------
The Computational Mechanics Co., Inc. (COMCO) is in search of a suitable
software developer for reservoir simulation R&D; work. COMCO is a
high-tech R&D; company located in Austin, Tx and has engaged in
pioneering research in computational mechanics (solids, fluid,
electro-magnetism, etc.) and adaptive finite element technology for over
a dozen years. The position is aimed mainly at software development
leading to 3-phase/compositional reservoir flow simulation capabilities
using adaptive finite elements. (Also see www.comco.com)
The ideal candidate must possess a strong background in
3-phase/compositional reservoir flow simulation with adequate training
in finite element methods. Excellent coding ability (in C and FORTRAN),
teamwork, and self-motivation are necessary. The candidate must possess
a Ph.D. (or a M.S. with equivalent job experience) in a field directly
related to reservoir simulation. Hands-on experience with one or more
commercial reservoir simulator will be a strong plus.
The position is likely to become available around January-February of
1997.
Please mail your resume to:
   Computational Mechanics Co., Inc.
   7701 N. Lamar, Suite 200
   Austin, Tx 78752
   512 467 1382 (fax)
or e-mail (ascii text only, please) to:
   deb@comco.com

I am looking for a formula for equally spaced Lagrangian interpolation in
two dimensions.  I need a general formula for interpolation using
N-points.  I have found formulas for 2-, 3-, 4-, and 5-point interpolation
but have been unable to find a general formula.  Any references would be
appreciated.
-- 
Daniel A. Leatherwood
Graduate Research Assistant
Georgia Institute of Technology, Atlanta Georgia, 30332
Internet: gt7533b@prism.gatech.edu

Hi !
My problem involves solution of 12 ordinary differential equations with 
initial conditions.  Now these equations have 8 rate constants embedded 
in them, which I intend to vary in order to match the simulation plots 
with the experiemental observation.  I would appreciate if somebody could 
tell me if this can be done in MAPLE. If not, can you suggest some other 
way.
My email address is jayant@engr.uky.edu
Thanks
Jayant K. Gotpagar

> The point is not whether it makes algebraic sense but whether it behooves you
> to use that representation in a program.
> 
> If you represent _both_ operands of a complex multiplication as 2x2 matrices,
> and perform the naive matrix multiplication, you are doing twice the
> computational work by computing two redundant values and using more
storage. It
> is a wasteful representation in both time and space.
> 
> You can avoid some of the computational work by allowing one of your operands
> to be a column vector, in which case, a multiplication of (a + ib) * (c + id)
> would be
> 
>         | a  -b | | c |
>         | b   a | | d |
> 
> However, this is still less than optimal. Space is wasted to store the
> left operand, and your compiler will  never  clue in to the fact that in your
> matrices, the upper left is always the same as the lower right and lower left
> is the additive inverse of the upper right. It will generate code to
> redundantly fetch the value 'a' from separate objects, ditto for b.
> 
> I think that this was Bill Stockwell's point; he was not disputing the 
> algebraic correctness of representing complex numbers as matrices, was he?
> 
> Of course, you may not care about efficiency, and using 2x2 matrices can save
> you programming time if a matrix library is already available to you. The
> saving in programming time can be more significant than a saving in memory
> or computing time.
Using matrixes instead of complex nums is interesting when you use matrix
for something other in you programs.
Especially in dealing with anlytic geometry...
If not, better use a+bi... Easier.
-- 
M.TIBOUCHI
Mystical Queror of Transcendental Nums (n'other stuffs like that ;-)
>"e^(i.pi) + 1 = 0", Euler
>The shorter poem if poetry puts real together with imaginary.

Daniel Zagar wrote:
> 
> I am writing a serial interface and i need the exact information about
> representation of floating point numbers, ie bit patterns etc.
> 
>   What is the standard on Windows NT?
> 
NT uses the IEEE double Standard.  here's a C structure to show the
basic bit pattern:
struct IEEEDouble{
  unsigned short Mant[3];
  unsigned short Mant4:1;
  unsigned short Mant3:1;
  unsigned short Mant2:1;
  unsigned short Mant1:1;
  unsigned short Exp  :11;
  unsigned short Sign :1;
};
Most good hardware architecture textbooks will explain differing
formats.
>   What is the standard on IRIX?
> 
> Information about reference manuals with IEEE or corresponding standard
> numbers or is also needed.
> 
> --
> Daniel Zagar
> Cresita Engineering AB
> 
> addr:   Box 22226               e-mail: dza@cresita.se
>         S-250 24 Helsingborg    phone:  +46 - (0)42 25 32 31
>         Sweden                  fax:    +46 - (0)42 25 32 99

Octave version 2.0 is now available for ftp from ftp.che.wisc.edu
in the directory /pub/octave.  Diffs from the previous release are not
available because they would be quite large.
This is a major new release and includes many new features.
User-visible changes since the last release are listed in the file
NEWS, which is included in the distribution and available from
ftp.che.wisc.edu in the file /pub/octave/NEWS.  The ChangeLog files in
the source distribution contain a more detailed record of changes
made since the last release.
Most bugs reported since the release of version 1.1.1 have been fixed.
You can help make Octave more reliable by reporting any bugs you find
to bug-octave@bevo.che.wisc.edu.
What is Octave?
---------------
Octave is a high-level interactive language, primarily intended for
numerical computations that is mostly compatible with Matlab.
Octave can do arithmetic for real and complex scalars and matrices,
solve sets of nonlinear algebraic equations, integrate functions over
finite and infinite intervals, and integrate systems of ordinary
differential and differential-algebraic equations.
Octave uses the GNU readline library to handle reading and editing
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The Octave distribution includes a 200+ page Texinfo manual.  Access
to the complete text of the manual is available via the help command
at the Octave prompt.
Two and three dimensional plotting is fully supported using gnuplot.
The underlying numerical solvers are currently standard Fortran ones
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of C++ classes.  If possible, the Fortran subroutines are compiled
with the system's Fortran compiler, and called directly from the C++
functions.  If that's not possible, you can still compile Octave if
you have the free Fortran to C translator f2c.
Octave is also free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation.
-- 
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jwe@bevo.che.wisc.edu
University of Wisconsin-Madison
Department of Chemical Engineering
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Hi everybody,
I am new to this group.
I have a question.
Is there a formula using which one can calculate
    1 + x + x^2 + x^3 + ...... + x^n
Given values for x and n, I would like to calculate the
progressive expression using a formula (instead of calculating
it iteratively).
Thanks for all the help,
George Clement
gclement@imonics.com

George Clement wrote:
> 
> Hi everybody,
> 
> I am new to this group.
> 
> I have a question.
> 
> Is there a formula using which one can calculate
>     1 + x + x^2 + x^3 + ...... + x^n
> 
> Given values for x and n, I would like to calculate the
> progressive expression using a formula (instead of calculating
> it iteratively).
> 
> Thanks for all the help,
> 
> George Clement
> gclement@imonics.com
Hi,
are you sure you didn't have that in high-school? It's a finite
geometric series with value
               (1-x^(n+1))/(1-x)
-- 
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

fearlessfd@aol.com (FEARLESSFD) writes:
> From: fearlessfd@aol.com (FEARLESSFD)
> Newsgroups: sci.math.num-analysis
> Subject: Re: Center of gravity...
> Date: 14 Dec 1996 04:37:01 GMT
> Organization: AOL http://www.aol.com
> Distribution: inet
> Message-ID: <19961214043600.XAA08119@ladder01.news.aol.com>
> References: <58kn4c$1iei@fidoii.cc.lehigh.edu>
> NNTP-Posting-Host: ladder01.news.aol.com
> X-Admin: news@aol.com
> 
> The COG of any triangle is given by the intersection of the lines
> bisecting the angles.
> 
This is plainly wrong! 
Alois
> fred a.
-- 
___________________________________________________________________________
Alois Steindl,                  Tel.: +43 (1) 58801 / 5529       
Inst. for Mechanics II,         Fax.: +43 (1) 5875863
TU Vienna,
A-1040 Wiedner Hauptstr. 8-10   Email: Alois.Steindl+Mechanik@tuwien.ac.at
___________________________________________________________________________