Subject: Re: 3D surface representation
From: suter@fawlty8.eng.monash.edu.au (Mr D. Suter)
Date: 10 Jan 1997 02:38:12 GMT
In article <32D5AD81.1981@lanet.lv> snap writes:
>Hi!
> Does anybody knows some nice surface approximation
>in 3D which contains exactly pre-given set of points.
> 2D analogue is piecewise polynomial spline
>curve which has continuous 1st & 2nd derivatives
>and contains pre-given set of marker points.
> What I expect in 3D is continuity of 1st & 2nd derivatives.
>Thanx in advance!!!
The spline in 2D, to which you refer, is the cubic spline
which has an energy function minimization property
(integral of square of second derivs). The usually quoted
3D analogue (2D surface in 3D) is the thin-plate spline.
This, however, only has 1st deriv continuity of the data points.
It is defined by minimizing the integral of the a combination of
second derivatives of the function. You would have to use a smoothness
functional that had third order derivatives to get second order
continuity at the data points. All of this is in Grace Wahba's
book - Spline Models for Observational Data, SIAM Press.
BTW for a number of reasons, most people take another route
to generalising the cubic spline - tensor products of
cubic splines. The background theory (minimizing semi-norms)
is not as elegant, and the the functions are not isotropic,
but the theory is usually much easier to understand
and the matrix systems reasier solve.
regards
d.s.
--
David Suter - Dept. of Electrical and
Computer Systems Engineering, Monash University,
Clayton, Vic. 3168, Australia
ph 9905 5682 Fax 9905 3454
Subject: Final call for papers IEEE SMC 1997 Orlando
From: fridrich@binghamton.edu ()
Date: 9 Jan 1997 18:12:25 GMT
FINAL CALL FOR PAPERS
__________________________________________________________________
1997 IEEE International Conference on Systems, Man, and Cybernetics
Hyatt Orlando, Orlando, Florida, USA * October 12-15, 1997
Computational Cybernetics and Simulation
__________________________________________________________________
I am organizing a track at the below conference. The track will
have 2-3 sessions directed towards applied chaotic systems for
simulation, data mining, control, image processing and encryption,
and possibly other related topics connected with chaos.
Jiri Fridrich
Center for Intelligent Systems
SUNY Binghamton, NY 13902-6000
E-mail: fridrich@bingsuns.cc.binghamton.edu
Ph/Fx: 607-777-2577
___________________________________________________________________
Preliminary Announcement
1997 IEEE International Conference on Systems, Man, and Cybernetics
Hyatt Orlando, Orlando, Florida, USA * October 12-15, 1997
Computational Cybernetics and Simulation
Location: October 12-15, 1997 at the Hyatt Orlando in Orlando, FL.
Room rate: $105.00 per night, single or double.
Located in the heart of Central Florida. Easy access to
Disney World, Sea World, Universal Studios. Golf course,
a health club, tennis courts, swimming pools, restaurants.
Theme: Computational Cybernetics and Simulation has been
selected to emphasize the growing importance of compu-
tational methods and modeling tools in the design,
analysis, and control of complex systems. Presentations
dealing with theoretical perspectives, new computational
tools, new paradigms in simulation, and innovative
modeling applications are encouraged.
Organizing Committee:
General Chair, James M. Tien, RPI
Technical Programs Chair, Charles J. Malmborg, RPI
Technical Arrangements Chair, Julia Pet-Edwards, Uni-
versity of Central Florida
Functional Arrangements Chair, Mansooreh Mollaghasemi,
University of Central Florida
Promotional Programs Chair, Mark J. Embrechts, RPI
Call for Contributed Papers:
The Technical Programs Committee solicits papers for pre-
sentation at the conference. All papers will be reviewed by
up to three referees for technical merit and content on the
basis of an abstract of no more than 300 words. Papers
accepted for presentation will appear in the Conference
Proceedings. All abstracts must have a cover page containing
the title of the paper along with the names, affiliations,
and complete mailing addresses of all authors, as well as
a rank-ordered list of the three designated topic areas
most closely related to the paper. The cover sheet should
list the two-digit number along with the name of each of
the three designated topic areas. All correspondence will
be directed to the first named author unless indicated
otherwise. We regret that e-mail abstracts of paper
submissions cannot be accepted. Six pages will be allocated
in the Proceedings for each accepted paper. Papers which
exceed this length will be charged on a per page basis.
Each paper presentation should take no more than 20-30 min.
Call for Invited Sessions / Tracks:
Invited Sessions (each comprised of 4-6 papers) and
invited tracks (each comprised of at least 2 sessions) are
solicited in all topic areas. Survey papers and/or case
studies could form the basis of invited sessions. Each
prospective session/track organizer must submit a proposal
including the title of the session/track, a rank-ordered
list of the three topic areas most closely related to the
session/track, and a list of authors with paper titles and
abstracts.
Call for Conference Tutorials:
The Technical Arrangements Committee solicits proposals
for half-day tutorials or workshops which are related to
the conference theme. An honorarium will be provided for
each tutorial based on the number of registered attendees.
Important Dates:
FEBRUARY 15, 1997 (FIRM) Deadline for 3 copies of
contributed paper abstract (with topic area designations)
MARCH 15, 1997 (FIRM) Deadline for 3 copies of
invited session/track proposal (with topic area
designation)
APRIL 15, 1997 (FIRM) Acceptance/rejection notification
of contributed paper abstracts and invited session/track
proposals
JUNE 15, 1997 Deadline for final "camera ready"
paper and author preregistration
DESIGNATED TOPIC AREAS:
1 Computational Cybernetics
11 Biocybernetics
12 Statistics and Forecasting
13 Pattern Recognition and Classification
14 Image Processing and Classification
15 Fuzzy Systems
16 Neural Networks and Computational Intelligence
17 Data Mining and Knowledge Discovery
18 Optimization, Heuristics, and Search Methods
2 Decision Systems
21 Cognitive Systems and Engineering
22 Desision and Conflict Analysis
23 Decision Support, Expert and Knowledge Systems
24 Management Information Systems
25 Medical Informatics and Decision Making
26 Multicriteria and Group Decision Making
27 Visualization, Multimedia, and Graphical Interfaces
28 Database and Software Engineering
3 Human-Machine Systems
31 Command and Control Systems
32 Human Computer Interaction and Virtual Reality
33 Human Factors in Design
34 Robotics
35 Quality and Productivity
36 Training Technology
37 Adaptive and Learning Systems
38 Machine Learning
4 Simulation
41 Animation
42 Continuous Simulation and Applications
43 Discrete Event Dynamic Systems
44 Output Analysis
45 Simulation Languages and Software
46 Simulation Training Systems
47 Military Simulation
48 Simulation Methodology
5 System Methods and Applications
51 Systems Modeling, Analysis, and Evaluation
52 Education and Multimedia
53 Communications and Transportation Systems
54 Energy and Environmental Systems
55 Health Care Systems
56 Service and Public Sector Systems
57 Military Systems
58 Manufacturing Systems and Petri Nets
**********************************************************************
| Jiri FRIDRICH, Research Associate, Dept. of Systems Science and |
| Industrial Engineering, Center for Intelligent Systems, SUNY |
| Binghamton, Binghamton, NY 13902-6000, Tel.: (607) 797-4660, |
| Fax: (607) 777-2577, E-mail: fridrich@binghamton.edu |
**********************************************************************
......................................................................
Remember, the less insight into a problem, the simpler it seems to be!
----------------------------------------------------------------------
Subject: Re: Need to handle Big Matrix (800x800) to use optimization algorithms
From: jmccarty@sun1307.spd.dsccc.com (Mike McCarty)
Date: 10 Jan 1997 03:06:49 GMT
In article ,
Gary Hampson wrote:
)In article <32C90B5C.64B1@public.ibercaja.es>, benigno
) writes
)>Hi,
)> I need to handle Big matrix of around 800 x 800 to implement
)> some optimization algorithms, I would use C++ libraries if
)> possible to use on BorlandC++ 4.5, but if there is any shareware
)
)Unless the matrix has some structure which allows many short cuts and
)reduced storage (eg Toeplitz), then just get on with coding it. 800*800
)is not that big (unless of course in the optimisation you need to
)evaluate A.x many times, or you have some time critical conditions.
)--
)Gary Hampson
800x800 is not that big? Assuming 64 bit reals, that works out to about 5
megabytes of data. Since he's usig BorlandC, that means he's more or
less stuck with the 640K of main RAM.
If you need that big a matrix, I suggest you may switch to DJGPP
(version of GNU CC) for the DOS machines. It automatically allows using
of virtual memory.
Mike
--
----
char *p="char *p=%c%s%c;main(){printf(p,34,p,34);}";main(){printf(p,34,p,34);}
This message made from 100% recycled bits.
I don't speak for DSC. <- They make me say that.
Subject: Re: multidim. secant method ?
From: spellucci@mathematik.th-darmstadt.de (Peter Spellucci)
Date: 10 Jan 1997 12:49:49 GMT
In article <32D4B701.15FB7483@ic.ac.uk>, Jorge Paloschi writes:
|> Uwe Schmitt wrote:
|> >
|> > hi,
|> >
|> > i try to solve some equation F(x)=0 numericaly.
|> > x = (x1,...,xn), F(x) = (f1(x),...,fm(x)).
|> > im not able to use a multidimensional newton-method, because
|> > im not able to compute the derivative DF ( F is computed
|> > by a simulation of a physical process).
|> > is there something like a "secant"-method in multi-dimensions ?
|>
|> Use Discrete Newton, that is, finite differences approximation to
|> Jacobian. If n is large and your F(x) has a sparse Jacobian you can then
|> use the CPR algorithm to minimize the number of function evaluations.
|>
|> Jorge
why not using Broyden's method ? discrete Newton is somewhat costly
Its main benefit comes from possible globalization of convergence
via damping (backtracking). The modified Secant method of Gragg&Stewart;
SINUM 13, 1976, may also be useful.
peter
Subject: Re: How to find eigenvalues of "bad" matrix
From: hwolkowi@orion.math.uwaterloo.ca (Henry Wolkowicz)
Date: Fri, 10 Jan 1997 14:58:35 GMT
In article <32D39E85.41C6@damtp.cam.ac.uk>,
Tom Chou wrote:
>Hello,
>
>I have an infinite, real, nonsymmetric square matrix
>of which I want to find the lowest 10 or so eigenvalues.
>I am taking larger and larger truncations and seeing if the eigenvalues
>converge. I am using balancing, then reduction to Hessenberg form, then
>use a QR algorithm as described in Numerical Recipes.
>
>However, for my particular matrix, I find that the eigenvalues don't
>quite converge at 40 X 40, where the algorithm uses too
>many interations and exits (the lowest eigenval. changes by ~5% in going
>from 20 X 20 to 40 X 40). . Looking at the qualitative trends, I figure
>I need about a 400 X 400 truncation in the worst cases.
>
>I think the problem is that the off diagonals get very large
>numerically. The matrix elements go as n^2*m^3, so numerically
>get very large as one goes down the diagonal (~n^5) or, far away from
>the diagonals.
>
>
>My questions are:
>
>(1) Are there analytical bounds on how large a matrix I
>need to take for a required accuracy in the lowest few
>eigenvalues? Where can I find theories about the convergence of
>the eigenvalues as the matrix is taken to be larger and larger?
>
>(2) What codes should I use? Can I simply reset the
>number of iterations in the Numerical Recipes routines
>without catastrophic consequences? Are there other
>routines/packages suited for this kind of matrix?
>
>(3) Now suppose that each matrix element now depends on a parameter,
>s. I want to plot the eigenvalues as a function of s. Are there
>theorems which can say when or when not any eigenvalues are degenerate?
>Or in particular, whether the lowest eigenvalue for one values of
>s=s0 can become larger that say the 2nd largest at s=s0
>at a different value s=s1? Is it possible to say that the lowest
>eigenval. is ALWAYS lower than the second lowest, for all s in
>some range?
>
>This problem is related to band structure/floquet matrics.
>Any suggestions on where to look for the answers will be greatly
>appreciated.
>
>Thx,
>
>Tom
>
It is not necessarily true that the eigenvalues will converge; you need
assumptions such as 'Hilbert Schmidt' operator.
There are several references: a classical reference is the book by
Kantorovitch and Akilov - Functional Analysis - see Chapter 14.
There are several theorems there that show when and how to guarantee the
convergence. Another book is the book by Krasnoselkii - Approximate
Solutions of Operator Equations.
--
||Henry Wolkowicz |Fax: (519) 725-5441
||University of Waterloo |Tel: (519) 888-4567, 1+ext. 5589
||Dept of Comb and Opt |email: henry@orion.math.uwaterloo.ca
||Waterloo, Ont. CANADA N2L 3G1 |URL: http://orion.math.uwaterloo.ca/~hwolkowi
Subject: Re: Optimization of functions
From: borchers@nmt.edu (Brian Borchers)
Date: 10 Jan 1997 17:50:01 GMT
Is it better to minimize f(x) or maximize 1/f(x)? It depends on
the particulars of f.
First, it's important that f(x)>0.
Next, it's important to consider whether f(x) is convex, 1/f(x) is
concave, or both. If f(x) is convex and 1/f(x) is not concave,
then you're likely to be better off minimizing f(x) instead of
maximizing 1/f(x). For example, f(x)=e^(x^2)+0.0001 is convex,
while 1/f(x) is *not* concave.
It's also important to consider how big the higher order derivatives
of f(x) are. For example, suppose that Q is a positive definite
matrix, b is a vector, c is a scalar constant and f(x)=x'Qx+b'x+c.
Using Newton's method, you can find the minimum in one iteration,
because f is strictly quadratic. If you try to maximize 1/f(x),
you'll find that Newton's method will take more iterations, because
1/f(x) isn't strictly quadratic.
Another issue is that depending on the function, minimizing f(x) or
maximizing 1/f(x) might be a much better conditioned problem.
--
Brian Borchers borchers@nmt.edu
Department of Mathematics http://www.nmt.edu/~borchers/
New Mexico Tech Phone: 505-835-5813
Socorro, NM 87801 FAX: 505-835-5366
Subject: Re: How to determine what values are small enough to be set to zero in SVD?
From: nmm1@cus.cam.ac.uk (Nick Maclaren)
Date: 10 Jan 1997 21:07:02 GMT
In article <5b65mi$9tc@oxywhite.interaccess.com>,
Billy Leung wrote:
>
>In SVD solution of linear equation, one often has to zero out certain
>small values to proceed. How do you actually determine a value is small
>enough in reference to a particular problem?
With some difficulty! It clearly depends very much on the exact problem
(including the precise details of the matrix properties), but it also
depends on the algorithm used.
Some 25 years ago, I needed to get the square root of a positive,
semi-definite real matrix expressed in lower triangular form. Studying
Wilkinson and Reinsch (or maybe just Wilkinson) indicated to me that
both Gaussian elimination and Cholesky decomposition could be used for
this, and that the former was slightly more resilient against singular
values.
In both cases, the best way to solve the problem was to add a diagonal
matrix with elements like K*order*max(element)*macheps, but K was about
twice as big for Cholesky. I cannot now remember the exact criteria.
Since then, fancy SVD methods have been developed, and I believe that
some of them are more stable. But the same principles apply.
Nick Maclaren,
University of Cambridge Computer Laboratory,
New Museums Site, Pembroke Street, Cambridge CB2 3QG, England.
Email: nmm1@cam.ac.uk
Tel.: +44 1223 334761 Fax: +44 1223 334679
Subject: Re: Good book for Applications of Group Theory?
From: odonovan@physun.cis.mcmaster.ca (Chris O'Donovan)
Date: 10 Jan 1997 14:09:42 -0800
In article ,
Lou Pecora wrote:
] At present I am using an old version of Tinkham's book on Group Theory and
] Quantum Mechanics...
I liked: Symmetry in the Solid State, R. S. Knox and A. Gold,
W. A. Benjamin, Inc., 1964, where on p. 41, when leading up to how the
irreps are projected out from a function, say that from the literature
the reader may have gained the impression that they ``are obtained by
luck, by educated guesses, or by black magic. The last is in fact the
correct method and its secret formula follows...''
Chris O'Donovan
Subject: Re: Important Dif.-Equation
From: vmhjr@frii.com (Virgil Hancher)
Date: 10 Jan 1997 22:45:02 GMT
In article <32d0543f.2177474@news.toppoint.de>, nase@toppoint.de (M.
Graff) wrote:
> I need the solution of this vector-differential equation:
> (It is very urgent!!!)
>
> ..
> r =-c*r/(|r|^3)
>
> r is a vector and c a constant, positive real number.
> ..
> (r is the acceleration of course)
>
> This is the important differential equation of the twobody-problem.
In the two body problem, the motion can be restricted to the plane
determined by the "radius" vector r and the velocity vector dr/dt.
Within that plane, the motion is that of a conic section with one focus at
origin (r=0).
The polar equation is r = A/(1-e*cos(Theta - ThetaZero)),
r is the SCALAR disance from origin,
Theta is the angle measured from fixed direction in the plane,
A,e and ThetaZero are constants determined by the initial conditions,
e is the eccentricity of the conic section.
There is no general solution for r as a function of time, in closed form.
However closed form solutions of r as a function of time do exist for
special cases, such as circles or parabolas.
Subject: Re: Matrix operator implementation in C++
From: Joe Pekarek
Date: Fri, 10 Jan 1997 08:46:40 -0800
Return the matrix by value, not by reference as shown below. You should also have
the copy constructor and the assignment operator (=) defined properly for your
matrix class. The return by value will create a temporary object on the stack,
which may not be very efficient for large matrices. For large matrices, use the
+= operator, or don't use operator overloading and create a function that takes
three arguments like AddMatrix(const Matrix& A, const Matrix& B, Matrix& C) where
C=A+B, but a temporary matrix is not required.
CivMatrix CivMatrix::operator + ( const CivMatrix& m )
{
CivMatrix g_iv( m_iRow, m_iCol );
for( int i=k0;i
> I want to implement a simple addition operator in C++ (Borland C++ 5.01).
> I was able to implement a += operator just fine, but the straight +
> operator poses a problem in returning a value that will not affect my
> existing matrix. The problem comes in creating an appropriate temporary
> matrix to return the new matrix value. As shown below, the obvious and
> erroneous answer (a local temporary) is inappropriate. How to I handle a
> global or static return matrix properly (that is, avoiding a memory leak)?
>
> Stephen
>
> // Example of what not to do:
>
> CivMatrix& CivMatrix::operator + ( const CivMatrix& m )
> {
> CivMatrix g_iv( m_iRow, m_iCol );
> for( int i=k0;i {
> g_iv.SetNull();
> g_iv.m_pMatrix[i] = m_pMatrix[i]+m.m_pMatrix[i];
> }
> return g_iv; // Opps, trying to return a local value...
> }
>
> // This implement seems to work fine:
>
> CivMatrix& CivMatrix::operator += ( const CivMatrix& m )
> {
> CInterval iv;
> for( int i=k0;i {
> iv.reset();
> iv = m_pMatrix[i]+m.m_pMatrix[i];
> m_pMatrix[i] = iv;
> }
> return *this;
> }
