Newsgroup sci.math.num-analysis 28958

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Given:
Two real continuous functions: f(x) and g(x), a rotation of g(x)about
the origin, and a bounding rectangle {(Xl, Yl), (Xh, Yh)}.
Find:
The all intersections of f and rotated g within the bounding rectangle.
Assume the existence of a root finder that works reasonably well over
the class of functions (non rotated) considered. Add restrictions to the
class of functions if necessary. Perfection is not expected, especially
in characterizing infinite intersections.
I need this problem solved (approximately) for a piece of educational
software I am trying to write. Any suggestions appreciated.
Thanks.
Fred Siegeltuch
fbs@cenplus.com

Joel Shellman  wrote:
One of my students tried to use standard DASSL for solving index one 
problems (material & energy balances + phase equilibrium conditions: 3 DEs 
and ca. 30 AEs); no solution was found. It is not clear yet what was the 
problem. It seems like DASSL needs consistent initial conditions, but the 
problem that was tested was difficult. On the other side, a colleague of 
mine has used DASSL successfully with very large problems. In his case, the 
AEs where relatively simple.
I've been told that a DASSL derivative/extension named GREGPAK is supposed 
to solve more difficult problems (by professor Warren E. Stewart et al., 
Department of Chemical Engineering, The University of Wisconsin at 
Madison). This program is designed for solving DAEs including sensitivity 
analysis, PDAEs (converting the PDAEs to DAEs using the Method of lines), 
and generalized nonlinear parameter estimation. I haven't tested this 
program so far, but intend to do so.
>Has there been any good methods developed for numerical solution of
>DAE's?  Is there anywhere on the net that has information about it?  I
>read a book recently and it said there wasn't a good method for this
>yet.  The book is a few years old, so I'm wondering what the current
>situation is.
>
>Thanks,
>
>-joel
>
>-- 
>taotree Tutor and Stuff
>Math and Physics Solver and thoughts on Creativity
>http://www.geocities.com/CapeCanaveral/8103/

Optech Solutions would like to announce its new web page at:
http://www.wbm.ca/users/optimize/
This start up company is based on a super efficient global optimization
algorithm discovered whilst doing research into the protein folding
problem.
We look forward to being of service to the mathematical and scientific
research communities.
Best wishes,
Jim Pulfer
Optech Solutions

I am looking for solution for the following system of ODE
[A] x*x {y''}+([A]-[B]+Transpose[B]) x {y'} +([D] x*x -[C]) {y} =0
where [A], [D] and [C] are positive definite N*N matrices,
[B] is a general N*N matrix.
{y} is to be solved as a function of x in the range 0<= x <= x0
and in the range x0<= x up to infinity.
Although, it is a well understood problem in scalar case (N=1),
I could not find a reference for the matrix case.
Do anybody can solve this problem or know of a solution?
Any suggestions and references will be very welcome.
Thank you very much in advance.
Chongmin Song
Swiss Federal Institute of Technology Lausanne
Switerland

Hello,
I was hoping to be able to find pointers to the following question:
Given that I know the value of the integrals (all notation in TeX):
\int f(x) dx
and
\int x^2 f(x) dx
what can I say about the integral
\int exp(-d.x^2)f(x) dx
where d is some positive constant and the range of all the integrals are
from -\infty to \infty ?
Perhaps straightforward, but I am a little stuck right now. Being told
which book to go look at would be a fine response!
Thanks,
Arjendu
-- 
_____________________________________________________________________
Chemical Physics Theory Group | Dr. Arjendu K. Pattanayak            
University of Toronto         | email: arjendu.pattanayak@utoronto.ca
Toronto, Ontario              | Phone: 416 978 4651                  
Canada, M5S 3H6               | Fax:   416 978 5325                  
______________________________|______________________________________

	In article <329F1EEC.41C6@Sorry.Trying.to.avoid.spam>,
		Arjendu Pattanayak
			 wrote:
> Given that I know the value of the integrals (all notation in TeX):
>
> \int f(x) dx      and     \int x^2 f(x) dx
>
> what can I say about the integral
>
> \int exp(-d.x^2)f(x) dx
>
> where d is some positive constant and the range of all the integrals are
> from -\infty to \infty ?
	Differentiate \int exp(-d.x^2)f(x) dx with respect to d, getting
 \int -x^2 exp (-d.x^2)f(x) dx.  (Here you have to worry about whether the
interchange in the order of differentiation and integration is justified,
-- see something like Rudin's _Principles_of_Mathematical_Analysis_.)
The value of this expression at d=0 is \int -x^2 f(x) dx, and you know the
value of that.  If you _don''t first differentiate with respect to d, but
just evaluate the integral \int exp(-d.x^2)f(x) dx at d=0, you get
\int f(x) dx, and you know the value of that.  So if you define a function
g(d) = \int exp(-d.x^2)f(x) dx then you know the values of g(0) and g'(0).
(Maybe you can say a bit more -- think carefully about Fourier
transforms.)
	Mike Hardy
Michael Hardy
hardy@stat.umn.edu

	In article <329F1EEC.41C6@Sorry.Trying.to.avoid.spam>,
		Arjendu Pattanayak
			 wrote:
> Given that I know the value of the integrals (all notation in TeX):
>
> \int f(x) dx      and     \int x^2 f(x) dx
>
> what can I say about the integral
>
> \int exp(-d.x^2)f(x) dx
>
> where d is some positive constant and the range of all the integrals are
> from -\infty to \infty ?
	Differentiate \int exp(-d.x^2)f(x) dx with respect to d, getting
 \int -x^2 exp (-d.x^2)f(x) dx.  (Here you have to worry about whether the
interchange in the order of differentiation and integration is justified,
-- see something like Rudin's _Principles_of_Mathematical_Analysis_.)
The value of this expression at d=0 is \int -x^2 f(x) dx, and you know the
value of that.  If you _don''t first differentiate with respect to d, but
just evaluate the integral \int exp(-d.x^2)f(x) dx at d=0, you get
\int f(x) dx, and you know the value of that.  So if you define a function
g(d) = \int exp(-d.x^2)f(x) dx then you know the values of g(0) and g'(0).
(Maybe you can say a bit more -- think carefully about Fourier
transforms.)
	Mike Hardy
Michael Hardy
hardy@stat.umn.edu

I need help, especially with a program to solve the following equation
for X1 and X2:
A(J)*(1 + K/X1)**(-X1) = (1 + X2)**(-K/X2)
A(J) is a vector of 7 elements 
K is a constant.
A(J) = (2.0, 1.2, 3.4, 5.6, 8.0, 8.3, 9.1)'
I think this can be solved with a Nonlinear least Square approach
(unconstrained minimization problem). I am looking for any help,
especially a fortran program to solve it. 
Thanks
Luke

Al Gerheim (gerheim@sonalysts.com) wrote:
: Harold Howe wrote:
: > 
: > I need a peak finding algorithm, and I have no idea where to
: > start looking for one.  What are some of the techniques used
: > to analyze sampled data.
: > 
: > If you have any advice I would appreciate it.
: > 
: 
G'day,
See "Numerical Recipes in C", Cambridge Press, ISBN 0-521-43108-5.
Chapter 10. Minimization or Maximation of Functions will give code and tell 
you more than you wanted to know ;-]
Lionel at Byron Bay Australia.

fred@genesis.demon.co.uk (Lawrence Kirby) wrote:
>In article  edb@syd.dms.csiro.au "Ed Breen" writes:
>
>>It appears that parameters of type array of T are converted
>>to pointer to T at their point of declaration, and this is because
>>C does not pass arrays. However, a local or a global variable
>>of type array of T, does not get converted to pointer to T until
>>it is used in an expression and if it is not an 
>>operand to the sizeof operator.
>
>Or the & operator.
>
>>I also feel that this is an
>>inconsistency of the C language
>
>It is consistent in that passing an apparent actual array arrgument and
>takeing a formal array parameter both imply that the argument/parameter
>is really a pointer. How would you propose to change this without making
>a *major* change to the language to make arrays first class objects and
>passable directly as function arguments?
I am not certain what, if any, type of backlash the following
options will generate, but here goes.
I have no objections to arrays and functions being 2nd class
citizens. Although, given that structures and unions have a higher
status, I would have thought, that it would be a simple matter to raise
arrays to the same level.
However, the following rules should work, while keeping arrays and
functions in 2nd class:
	A formal array parameter will be treated as its specified type
when used as an operand to the sizeof operator.
or even:
 	A formal parameter will be treated as its specified type, but
arrays and functions will be passed by reference only.
>
>Arrays always "evaluate" to a pointer to their first element (& and
>sizeof don't take the value of their arguments, they take the address and
>size respectively). 
As this information can be obtained from each parameter's
specification, why lose it? Either be honest with the programmer and
make such parameter declarations illegal or accept what the programmer
has declared as the true type of the parameter.
>Function arguments are consistent with this.
>
>The rewrite rule that affects array and function formal parameters is
>certainly surprising but it makes everything work naturally.
>
Up to a point.
>>and especially since:  "parameters
>>are understood to be declared just after the beginning of the compound 
>>statement constituting the function's body" (K&R2; pg, 226). It
>>will be interesting to see what others think.
>
>I don't see that to be a problem. Formal parameters are clearly a different
>syntactic entity entity to local variables. Semantically the difference
>is in effect how they get initialised (in addition to the rewrite rule).
The intention of the above I believe, is to ensure that the scope of
the parameters are the same as the identifiers declared in the top
level of the function. I see no problems with a parameter retaining
its original specification. Why should information about a type be
lost? FAPP, the programmer should not be concerned about the rewriting
rule, all she needs to be concerned with is that arrays and functions
are passed, in essence, by reference only.
-- 
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