HDTenEightyP/NetNews huggingface dataset:
From: kjell@sccm.Stanford.EDU (Kjell Gustafsson)
Subject: Re: Automatic Time Step for an ODE
Organization: Computer Science Department, Stanford University, Ca , USA
Date: 6 Nov 92 12:01:16

In article <1992Nov5.110534.15386@edf.fr> engrand@clt13vf.der.edf.fr writes:
>
>I'm studying different methods to automatically change the size of a time step
>when solving a time-dependant ODE. Automatically means that the code should
>know when it has to use a larger or smaller time step, 
>according to what happens to the sytem. 
>
>I haven't heard on any book dealing with this problem (but I haven't looked
>very hard) ; is there any ?

I've studied this problem in my thesis "Control of Error and
Convergence in ODE Solvers", Kjell Gustafsson, Department of Automatic
Control, Lund Institute of Technology, Sweden, 1992". It turns out
that with some ideas from feedback control you can get a better
understanding of the stepsize adjustment problem and also design
improved algorithms. 

Part of the material (the one concerning explicit methods) is
published in ACM TOMS: "Control Theoretic Techniques for Stepsize
Selection in Explicit Runge-Kutta Methods", Kjell Gustafsson, 17:4,
1991, pp. 533-554.

Kjell

-------------------------------------------------------------------------------
    mail: Kjell Gustafsson, Department of Computer Science MJH309
          Stanford University, Stanford CA 94305, USA
  e-mail: kjell@sccm.stanford.edu
   phone: (415) 723-4269 (voice), (415) 723-2411 (fax)

--
-------------------------------------------------------------------------------
    mail: Kjell Gustafsson, Department of Computer Science MJH309
          Stanford University, Stanford CA 94305, USA
  e-mail: kjell@sccm.stanford.edu
   phone: (415) 723-4269 (voice), (415) 723-2411 (fax)
From: fsrmh1@acad3.alaska.edu
Newsgroups: sci.math.num-analysis
Subject: Euler's *Theorem* Proof?
Date: 10 Nov 92 18:30:28 GMT
Article-I.D.: acad3.1992Nov10.103028.1
Organization: University of Alaska Fairbanks

Euler's Theorem:  

Who Proved Euler's *Theorem*?

I have looked through many a book, card catalog, etc, and haven't found the
answer to the above.  If you know the answer, and source, I sure would
appreciate you telling me.  This is driving me crazy.

Please e-mail me direct, if you please.

Thanks, in advance.

Randy
randy@raven.alaska.edu
	or
sxrmh1@orca.alaska.edu
From: tokero@sample.eng.ohio-state.edu (Onur Toker)
Newsgroups: sci.math.num-analysis
Subject: Roots of polynomials
Date: 7 Nov 92 02:58:15 GMT
Article-I.D.: ee.1992Nov7.025815.19914
Organization: The Ohio State University Dept of Electrical Engineering


	I don't know whether this is an FAQ, but does anybody know which
algorithm MATLAB uses to find the roots of polynomials. If you know any
references on this or algorithms which works as good as MATLAB's please send
me by e-mail. Thanks.

	Onur TOKER
From: jhurst@amb4.ccalmr.ogi.edu (James Hurst)
Newsgroups: sci.math.num-analysis
Subject: what kind of matrix solvers do you recommend?
Summary: We do finite elements, 2-D and 3-D, what to plan on using?
Keywords: Survey, solvers, sparse, general, banded
Date: 7 Nov 92 01:10:15 GMT
Article-I.D.: ogicse.45401
Followup-To: jhurst@ese.ogi.edu
Organization: Center for Coastal and Land-Margin Research

I've just had a nasty time moving a sparse solver onto a Cray to support 
some chemistry/hydrodynamic finite element work.  The difficulty convinced
our group to give some thought to what math libraries we want to be using
in the next few years, both public and private domain.

In particular, several solvers, both public domain and commercial, failed
numerically on the speciation problem, much to my surprise.

Dongarra's LAPACK seems to be a common denominator for many folks, but it
doesn't cover all our needs, particularly large sparse systems.  Many of the
sparse solvers don't give much in the way of non-symmetric matrices, either,
which rules them out for our chemistry, if not our FE things.

So I want to survey the net with a few general questions about mid- to large 
sized matrix solvers.  Respond by email, and I'll summarize the results.


	What general matrix solvers do you use in you codes?  
		Why this solver?
		Are you happy with it?	

	If you do sparse matrix work, what solver do you use?  
		Why this solver?
		Is your problem symmetric?
		Are you happy with it?	

	If you do banded matrix work, what solver do you use?  
		Why this solver?
		Are you happy with it?	

Thanks for your help, back in a week or so.

					Cheers,

					Jim Hurst
					jhurst@ese.ogi.edu
Newsgroups: sci.math.num-analysis
From: jblee@giga.cs.umn.edu (Jaebum Lee)
Subject: polynomial root finding
Organization: University of Minnesota, Minneapolis, CSci dept.
Date: Thu, 5 Nov 1992 17:50:07 GMT

Hi,
I am looking for a subroutine to find all the roots(including complex) of
a polynomial with real coefficients. Does anybody out there have such a
subroutine? Any pointers wiil be appreciated.

Jaebum Lee
jblee@tera.cs.umn.edu
From: dbailey@wk49.nas.nasa.gov (David H. Bailey)
Newsgroups: sci.math.num-analysis
Subject: Fortran multiple precision package and translator
Date: 6 Nov 92 01:12:07 GMT
Organization: NAS, NASA Ames Research Center, Moffett Field, CA

Some of you may be aware of a multiprecision computation package and a
multiprecision Fortran translator that I have developed during the
past year or two.  I am now pleased to announce that this software has
been approved by NASA Ames for unlimited international distribution,
at no cost.  A brief description of this software is as follows:

The first package contains approximately 85 Fortran subroutines that
perform a variety of arithmetic operations and transcendental
functions.  The basic arithmetic routines are very efficient, and for
extra high levels of precision (about about 1000 digits), some
additional routines are available that employ advanced algorithms,
such FFT-based multiplication and the Borwein transcendental
algorithms, for additional speedup.  On some problems these routines
are over 200 times faster than certain other multiprecision tools.

However, as with other such packages, manually converting a program to
use these routines is a tedious and error-prone process.  To
facilitate such conversions, I have now developed a multiprecision
translator for Fortran programs.  By means of source directives
(special comments) placed in a standard Fortran-77 program, the user
declares the precision level and specifies which variables in each
subprogram are to be treated as multiprecision.  The translator
program reads this source program and outputs a program with the
appropriate multiprecision subroutine calls, which can then be linked
with the multiprecision package and executed.

This translator program supports multiprecision integer, real and
complex datatypes.  The required array space for multiprecision data
types is automatically allocated.  In the evaluation of computational
expressions, all of the usual conventions for operator precedence and
mixed mode operations are upheld.  Furthermore, most of the Fortran-77
intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce
true multiprecision values.

Both the multiprecision package and translator are written in highly
portable Fortran-77 and have been successfully implemented on a
variety of systems, ranging from parallel supercomputers to
workstations.

If anyone is interested in obtaining this software, plus the
accompanying documentation, send me a note, and I will respond by
e-mail.  I eventually intend to place this software on public media
such as netlib, but for the time being I am handling it myself, so
that any bug fixes or enhancements can be promptly distributed.  Since
it is a small but significant amount of trouble for me to respond,
please don't request unless you are somewhat serious about needing
this software.

David H. Bailey 
NASA Ames Research Center 
dbailey@nas.nasa.gov
Newsgroups: sci.math.num-analysis
From: tt@swamp.cacs.usl.edu (Thitipong Tanprasert)
Subject: Suggestion needed about constrained optimization
Organization: The Center for Advanced Computer Studies
Date: Fri, 6 Nov 1992 17:39:39 GMT

Hi,

    I'm not a math student and just started to know about numerical
optimization a couple of weeks ago. However, I need to optimize an upto
200 variables nonlinear (quadractic and maybe trigonometric) objective
functions under many nonlinear (trigonometric) constraints. I have no
expectation to find global optimum. Just hope to obtain some good
acceptable results. Would anyone please help suggesting a reliable 
constrained optimization method that I may program to deal with my
problem. I was suggested about Penalty Function and think it's quite
interesting. However, I have no idea if some other methods will
work better (generally). Also, if I use Penalty Function method, what
unconstrained optimization method should I attempt to implement? Is
there a ftp-able software about this that I may use directly without
having to program myself?


Any suggestion would be very appreciated,

T. Tanprasert


Newsgroups: sci.math.num-analysis
From: walsteyn@fys.ruu.nl (Fred Walsteijn)
Subject: Re: Automatic Time Step for an ODE
Organization: Physics Department, University of Utrecht, The Netherlands
Date: Tue, 10 Nov 1992 17:26:08 GMT

In <KJELL.92Nov9164250@simplicity.Stanford.EDU> kjell@simplicity.Stanford.EDU (Kjell Gustafsson) writes:

>The relation between the stepsize and the error may be quite different
>than the normally assumed asymptotic form. Part of this "deviation"
>has structure and can be modeled. By exploiting these models one
>arrive at a stepsize selection rule that results in smoother stepsize
>(and error) sequences as well as fewer stepsize rejections than the

Does this increase robustness of the error estimate in cases
where the right hand side is discontinuous ??

Thanks,
-----------------------------------------------------------------------------
Fred Walsteijn                                | Internet: walsteyn@fys.ruu.nl
Institute for Marine and Atmospheric Research | FAX:      31-30-543163
Utrecht University, The Netherlands           | Phone:    31-30-533169
Newsgroups: sci.math.num-analysis
From: katholi@willis.cis.uab.edu (C.R. Katholi)
Subject: Code for Rank Revealing QR Factorizations
Organization: University of Alabama at Birmingham
Date: Thu, 12 Nov 1992 21:56:33 GMT

     I think that I saw a notice somewhere not too long ago concerning
an implementation of the rank revealing QR factorization described by
T. Chan, "Rank Revealing QR Factorizations", Linear Algebra and Its
Applications, (1987). Can anyone point me to a place where I can obtain this
code, preferably by ftp. Please send responses to   katholi@cis.uab.edu.
     Thank you in advance for your help. 
Newsgroups: sci.math.num-analysis
From: kjell@sccm.Stanford.EDU (Kjell Gustafsson)
Subject: Re: Automatic Time Step for an ODE
Organization: Computer Science Department, Stanford University, Ca , USA
	<KJELL.92Nov9164250@simplicity.Stanford.EDU>
	<1992Nov10.172608.25322@fys.ruu.nl>
Date: 10 Nov 92 11:59:06

In article <1992Nov10.172608.25322@fys.ruu.nl> walsteyn@fys.ruu.nl (Fred Walsteijn) writes:

Fred>   In <KJELL.92Nov9164250@simplicity.Stanford.EDU>
Fred>   kjell@simplicity.Stanford.EDU (Kjell Gustafsson) writes: 
Fred>
Fred>   >The relation between the stepsize and the error may be quite different
Fred>   >than the normally assumed asymptotic form. Part of this "deviation"
Fred>   >has structure and can be modeled. By exploiting these models one
Fred>   >arrive at a stepsize selection rule that results in smoother stepsize
Fred>   >(and error) sequences as well as fewer stepsize rejections than the
Fred>
Fred>   Does this increase robustness of the error estimate in cases
Fred>   where the right hand side is discontinuous ??

No, not really! If you have a right hand side including
discontinuities you should use an integration method designed to
handle that. This normally requires you to supply some kind of
indicator function. The integration method applies a root finder to the
indicator function to resolve where the discontinuity occurs, and then
chooses an appropriate stepsize sequence to pass the discontinuity.
A good example of such a code is DDASRT written by Linda Petzold.

When dealing with discontinuous right hand sides it is important to be
careful in the modeling. For certain types of discontinuities one can
determine in beforehand at what time instance the discontinuity
occurs, e.g. discontinuous input signals, simulation of combined
sampled and continuous-time systems, etc. The simulation can then be
handled as a sequence of continuous problems.

Strategies that count on the stepsize control to resolve the problem
with discontinuities often lead to inefficiency (it may take a lot of
rejected steps to pass the discontinuity) or inaccuracy (some codes
will reduce the stepsize to a minimum value and then use it to pass
the discontinuity irrespective of the output of the internal error
estimator).

Kjell
--
-------------------------------------------------------------------------------
    mail: Kjell Gustafsson, Department of Computer Science MJH309
          Stanford University, Stanford CA 94305, USA
  e-mail: kjell@sccm.stanford.edu
   phone: (415) 723-4269 (voice), (415) 723-2411 (fax)
From: moshier@world.std.com (Stephen L Moshier)
Newsgroups: sci.math.num-analysis
Subject: Re: wanted: ftp site for multiprecision (in C and Fortran )
Date: 7 Nov 92 00:47:26 GMT
Organization: The World Public Access UNIX, Brookline, MA


  There are at least three such packages in netlib (research.att.com).
Two Fortran programs are in netlib/toms, and there is a C suite
in netlib/cephes.
From: srw@horus.ps.uci.edu (Steven White)
Newsgroups: sci.math.num-analysis
Subject: Re: Arnoldi Method
Date: 13 Nov 92 18:52:04 GMT
Reply-To: srw@horus.ps.uci.edu (Steven White)
Organization: University of California, Irvine

In article <1992Nov13.003909.27705@marlin.jcu.edu.au>, maawg@marlin.jcu.edu.au (Andrew Gill) writes:
|> Hi.  Can anyone give me some textbook references to the Arnoldi method
|> for eigenvalue compuatation ?  I have a complex matrix and want that
|> eigenvalue with the largest imaginary part. 
|> 
|> ADVthanksANCE
|> 
|> Andrew Gill
|> maawg@marlin.jcu.edu.au

Youcef Saad, Numerical Methods for Large Eigenvalue Problems,
Manchester Univ Press, New York, 1992, QA188.S18

Good book.
Newsgroups: sci.math.num-analysis
From: tokero@bode.eng.ohio-state.edu (Onur Toker)
Subject: Repost; Help wanted about root finding algorithms
Organization: The Ohio State University Dept of Electrical Engineering
Date: Sat, 7 Nov 1992 17:37:26 GMT

Does anybody know very good root finding algorithms such as ones used
in MATLAB or other numerical analysis tools. I know the book called
'Numerical Recipies in ***' but I want much faster, and reliable 
algorithms. If you know any references please let me know.

Thanks

TOKER

e-address=tokero@ee.eng.ohio-state.edu
From: sjm@dciem.dciem.dnd.ca (Stewart Moorehead)
Newsgroups: sci.math.num-analysis
Subject: Solution of matrix equation AX=XB
Date: 12 Nov 92 14:17:11 GMT
Distribution: na
Organization: Defence and Civil Institute of Environmental Medicine


 I am recording the 6D position (x,y,z,roll,pitch,yaw) of an object
 using two independant devices. Since these devices have different
 reference frames a transformation matrix, call it X, must be
 calculated. To calculate X, the equation AX=XB must be solved, with A
 and B being known 4x4 matrices. I have found two methods which claim to
 solve for X. They were proposed by Roger Tsai and Reimar Lenz (June
 1989 IEEE Transactions on Robotics and Automation) and by C. C. Wang
 (April 1992). Both of these methods work if I pre-define X and create
 some 'cooked' data around it, however when I use actual data that was
 recorded using teh devices I get an incorrect answer. The devices being
 used are any two of : Northern Digital's Optotrak, Logitech's 3D mouse,
 and Polhemus Fastrak. I feel that the inherent error in these devices
 may be too great for the methods being used.
 I would appreciate it if anyone has information regarding these methods
 or the devices being used. If anyone has solved a similar problem
 please respond.
 You can send mail to sjm.dretor.dciem.dnd.ca
From: jonathan@geop.ubc.ca (Jonathan Thornburg)
Newsgroups: sci.math.num-analysis
Subject: Re: Gauss/Lobatto Quadrature Code
Summary: netlib has it: "send gaussq.f from go", "send index from quadpack"
Keywords: netlib integrate quadrature quadpack go golden oldies fortran
Date: 11 Nov 92 19:37:17 GMT
Article-I.D.: cs.1drnddINNn2q
Distribution: inet
Organization: University of B.C. Geophysics & Astronomy
NNTP-Posting-Host: rubis.astro.ubc.ca

In article <+kcqmdd@lynx.unm.edu> warsa@polaris.unm.edu (j warsa) writes:
>In the past several years, I have seen maybe ten or twenty requests for
>Gauss quadrature generating codes, and related things like numerical 
>integration programs. I have written FORTRAN codes that generate the
>Gauss and Lobatto quadratures, and other codes that perform 1- and 2-D 
>integration using these quadratures. In response to several of the requests,
>I mailed these programs directly to those who asked. 
>
>Becuase of the numerous requests for such programs, I thought that there may 
>not be any available in the traditional math library archives (like netlib, 
>etc.). I was wondering if anyone in this group could tell me what is available,
>and whether I should make my codes available to others via netlib, or some 
>other software repository. If you think I should, what is the procedure for 
>doing so?

If I may slightly plagarize a well-known (and doubtless copyrighted)
computer ad,

	netlib has it now!

(Sorry, couldn't resist :-) ...


Seriously, netlib has quite a bit of (excellent) Gaussian quadrature
software:
- QUADPACK is a FORTRAN subroutine package for the numerical
  computation of definite one-dimensional integrals.  It has
  a variety of subroutines in both single and double precision,
  based on various automatic and non-automatic Gaussian
  quadrature integrators.  Try "send index from quadpack"
  and/or "send readme from quadpack" for more info.
- The "golden oldies" library contains a routine for computing
  the nodes and weights for a variety of Gaussian-type quadrature
  rules.  Again, it comes in both single and double precision.
  Try "send index from go" or "send gaussq.f from go" for more
  info.


- Jonathan Thornburg
  <jonathan@geop.ubc.ca> through mid-November 92, then
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  [for a few more months] UBC / {Geophysics & Astronomy, Physics}
  [then through Aug/92] U of Texas at Austin / Physics / Center for Relativity
From: mek@jpl-devvax.jpl.nasa.gov (Mike Ketchmere)
Newsgroups: sci.math.num-analysis
Subject: REQ: Root finder to find zeroes of single equation f(x,y)=0
Date: 11 Nov 92 05:51:11 GMT
Article-I.D.: jpl-devv.1992Nov11.055111.17644
Organization: Jet Propulsion Laboratory (NASA)

I'm looking for a multi-dimensional zero-finding implementation to find the 
roots of a single equation f(x,y)=0.  Any hints on where to find one
would be appreciated.

Mike
mek@thyme.jpl.nasa.gov
Newsgroups: sci.math.num-analysis
From: mclean@dinsdale.dinsdale.phy.queensu.ca (Alastair McLean)
Subject: Numerical Programming in Objective C
Organization: Queen's University, Kingston
Date: Mon, 9 Nov 1992 15:37:42 GMT

I posted the following request in comp.lang.objective-c and got no
responce. Either no one reads comp.lang.objective-c or no one is using
Objective C for numerical work. I find the latter hard to believe.
There was an interesting posting in comp.lang.c++ (and in this news group)  
recently entitled

"Index of free C or C++ source code for numerical computation"

from Ajay Shah. My intent was to locate or collate a similar list for
Objective C.

___________________________ Repeat Request_________________________

DO SCIENTIFIC OBJECTS EXIST ?
I am considering doing some numerical programming in objective C and I  
would be interested to find out to what extent libraries of scientific  
(i.e. non GUI) objects are already available. After all that is the idea  
behind reusable software components. I am particularly interested in  
implementations of matrices and vectors with corresponding method  
functions for accessing elements, changing elements, adding, subtracting,  
inverting etc. I am interested in both stand alone implementations or  
implementations that may use Stepstone's Foundation package or NeXTs  
objective C as a starting point (I will be working with a NeXT).
 
INFORMATION ABOUT SCIENTIFIC PROGRAMMING WITH Objective C ?
I would also be interested in any references, texts or articles, that deal  
with the problems associated with scientific programming, i.e interfacing  
with Numerical Recipes in C or other numerical libraries. 

I will collate the information and post it at later time.
Thanks
Alastair McLean
__________________________________________________________________________
alastair@hecate.phy.queensu.ca
NeXTmail accepted
Newsgroups: sci.math.num-analysis
From: ismaeil@qucis.queensu.ca (Ossama Ismaeil)
Subject: Non-linear Inequality Constraint
Organization: Computing & Information Science, Queen's University at Kingston
Date: Thu, 5 Nov 1992 19:53:34 GMT



Hello !

   I wondered if any one can tell me about any method to solve an obtimization
   problem that has a non linear optimization function and non-linear 
   inequality constraints. The problem can be described as 

                  T
           Min   X  X  

      S.T         T 
                 X A X <= 0
                
  wher X is a vector and A is a square indefinite matrix.

  I would really appreciate it ver much. Thanks.


  Ossama
  e-mail   "ismaeil@qucis.queensu.ca"
Newsgroups: sci.math.num-analysis
From: mhosea@seas.smu.edu (Mike Hosea)
Subject: Re: Automatic Time Step for an ODE
Followup-To: sci.math.num-analysis
Keywords: Time Step, ODE, methods
Organization: SMU School Of Engineering and Applied Science
Date: Thu, 5 Nov 1992 19:32:50 GMT

In article <1992Nov5.110534.15386@edf.fr> engrand@clt13vf.der.edf.fr writes:
>
>I'm studying different methods to automatically change the size of a time step
>when solving a time-dependant ODE. Automatically means that the code should
>know when it has to use a larger or smaller time step, 
>according to what happens to the sytem. 
>
>I haven't heard on any book dealing with this problem (but I haven't looked
>very hard) ; is there any ?

All modern mathematical software for solving general ODE initial value problems 
control the step size automatically, though some require that you supply the
initial step size.  I don't know of any books written solely on this subject,
but you may wish to consult the relevant sections of

_Solving_Ordinary_Differential_Equations_I_, by Hairer, Norsett, and Wanner

_Solving_Ordinary_Differential_Equations_II_, by Hairer, and Wanner.

The first volume addresses nonstiff problems and the second stiff problems.
There should be enough references in those texts to get you started in the
literature.
-- 
Regards,
Mike Hosea (mhosea@seas.smu.edu)
Newsgroups: sci.math.num-analysis