mm-4149
===
Subject: Error in derivatives using taylor-expansion.
I've a question.
I can approximate a function with the first N expansion of a Taylor-series:
f_approx_(x_0+dx) ~ Sum_{n=0:{N-1}}f^n|x_0 * (dx)^n/n!
I know that the error is bounded by :
E < f^(n+1)|t * dx^N
Now is my question when I compute df_approx/dx and compare this to
df/dx, can it be proved that this error is also bounded.
I can write this error as:
E_2 = Sum_[n=N:Inf} n * f^n_x_0 * dx^ (n-1).
Can someone point me into teh right drirection.
In order to come to the latest equation I assumed that teh function is
infinitfely differentiable.
Maurice
===
Subject: Re: Error in derivatives using taylor-expansion.
> I've a question.
> I can approximate a function with the first N expansion of a
Taylor-series:
> f_approx_(x_0+dx) ~ Sum_{n=0:{N-1}}f^n|x_0 * (dx)^n/n!
> I know that the error is bounded by :
> E < f^(n+1)|t * dx^N
I think you mean:
|E| < |max_t(f^(n+1)(t)) * dx^{N+1}/(N+1)!|
> Now is my question when I compute df_approx/dx and compare this to
> df/dx, can it be proved that this error is also bounded.
Isn't your df_approx/dx equal to a Taylor series for df/dx with N-1
terms? You should then get a similar error bound but with dx^N/N!
instead of dx^{N+1}/(N+1)!.
---
Roy Stogner
===
Subject: Re: Looking for examples of bad data analysis
Bad data analysis in literature? Unfortunately there are alot of
examples.
One which comes to mind was in a control journal in the early 1990's on
neural networks. It claimed that the neural network gave a smoother
control
than the operator (it was trained to emulate the operator). They had about
7 points per system (operator, network). Once we did a little number
crunching, their claims were valid at a little under the 50 percent
certaintly level.
a p analysis, management was quite happy with it.
Michael
> For instructional purposes I am looking for true examples of bad data
> analysis in the published literature. A linear regression which was
> not robust and eventually misleading would be such an example. They
> can be in any field of science and may involve either real data or
> computer simulations, but should be transparent, instructive, and
> verifiable. Major historical errors are ideal.
> If you happen to know of any illustrative example that mislead many
> researchers, please let me know.
> Some disasters attributable to bad numerical computing
> http://www.ima.umn.edu/~arnold/disasters/
===
Subject: Re: Looking for examples of bad data analysis
> For instructional purposes I am looking for true examples of bad data
> analysis in the published literature. A linear regression which was
> not robust and eventually misleading would be such an example. They
> can be in any field of science and may involve either real data or
> computer simulations, but should be transparent, instructive, and
> verifiable. Major historical errors are ideal.
> If you happen to know of any illustrative example that mislead many
> researchers, please let me know.
this is probably not what you're looking for, but the analysis of
Pons and Fleischman (spelling?) that lead to the `discovery' of
cold fusion was wrong in many ways. I think that most of the
problems came from their ignorance of their measuring equipment
rather than from a misapplication of statistical theory. The
lesson here is that even correct statistical analysis won't
help if the 'data' is filled with non-random garbage. Maybe
you can work that into the lesson somewhere: Know your
equipment!.
Rob Komar
===
Subject: Re: Looking for examples of bad data analysis
FORGED_YAHOO_RCVD, QUOTED_EMAIL_TEXT, REFERENCES)
> ...the concern is how many cancers are induced by the
> radiation used to acquire the mammogram? The current official
> estimate is something like 1 in 10,000 (don't quote me) women
> who are screened yearly starting at age 40 will develop a cancer
> from the x-rays used in the screening proceedure. However, this
> estimate is based upon the so called linear no-threshold model
> which states assumes that if at a radiation dose of X, Y people
> out of a thousand develop cancer, then at a dose of 0.001X,
> 0.001Y people out of a thousand will develop cancer.
Sounds somewhat strange. Isn't it natural to assume the
probability to develop cancer due to a certain doze doesn't depend
on the amount of previously absorbed radiation (assuming the later
didn't induce cancer already)? If so, it would mean that given
the probability to develop cancer due to doze d is P(d), one has
P(kd) = 1 - (1 - P(d))^k. Of course, if P(d) is small enough this
is approximately linear. Is that the motivation for the linear
no-threshold model? However, you said the extrapolated data is
for extremely high d where P(d) might be not that small?
Squark
------------------------------------------------------------------
Write to me using the following e-mail:
Skvark_Nuclearsto@excite.exe
extension in the obvious way)
===
Subject: Re: Method for solving nonlinear system
You will probably find some informations here
http://www.library.cornell.edu/nr/bookcpdf/c9-6.pdf
Roland
> I need to write program to solve any nonlinear system.
> 1. Is then Newton method or some improvement/modification of simplest
Newton
> method.
> 2. How to guess initial values to improve convergence? Is there any
method?
> Peter
===
Subject: Re: Method for solving nonlinear system
> what BFGS stands for?
Broyden-Fletcher-Goldfarb-Shanno (that's off the top of my head,
so I may have misspelled one of the names). a web search for
BFGS and/or quasi-newton methods should turn up lots of hits
you might also want to look at the Levenberg-Marquardt technique
--
Mark Vaughan
____________
Visit the Numerical Methods in Pascal web page at
http://www-rab.larc.nasa.gov/nmp/fNMPhome.htm
===
Subject: Navier-Stokes / finite elements / pressure correction / start
values
Hi all!
I have implemented a finite element code for Navier-Stokes
equations (using a cascadic multilevel method). On each level
the equations are solved in a segregated (decoupled) form,
which requires a pressure correction step in each iteration.
This step is computed by a conjugate gradient method.
Taylor-Hood elements (3D) are used.
My problem is that this method does not always work because
the cg method for the presure correction does not converge.
I think the reason is that for some boundary coditions the
start values for the velocities do not satisfy the incompressibility
condition which makes the pressure correction equation unsolvable.
I read that the problem can be solved by a special handling of
the pressure (e.g. setting the pressure at the boundary to a value
near the boundary). How can do something like this for finite
elements?
Or is there another solution for the start value problem?
Andreas Stelter
--
Andreas Stelter ** http://www.astelter.de
===
Subject: nodal stress-strain calculation
dear all,
I have used the following method but I'm not so sure whether it is
the correct way. Please advise
{strain} = [B] * {u}
{stress} = [D][B] * {u}
{strain},{stress},{u} - nodal strain, stress and displacements
vectors, respectively
[B] - strain-displacement matrix evaluated at nodes.
Alvin
===
Subject: Projection of bivariate guassian function?
Is there anyone who knows of some formula how to calculate the
projection of a bivariate gaussian function under an arbitrary angle
theta, in function of this angle theta, sigma_x, sigma_y and sigma_xy?
Also, some reference to a textbook on this matter would be helpfull...
Filip
===
Subject: Redundant Network Paths, How to Identify
If this is addressed to the wrong group, please let me know of a more
appropriate destination.
I am working with some project management software that performs
scheduling of tasks. When schedulers define a network of tasks or
links, they use a table with the following structure: PE (predecessor
event), SE (successor event) and TYP (constraint type). PE and SE are
integers. TYP is one of 4 items: FS, SF, SS, FF -- indicating a
Finist-to-Start, Start-to-Finish, Start-to-Start, or Finish-to-Finish
relationship between the PE and SE).
If there is no SE present, the table entry is a task.
If there is an SE present, the table entry is a constraint and a TYP
must also be present.
A simple FS network like this: 1------2------3
Would have this table:
PE SE TYP
1
2
3
1 2 FS
2 3 FS
These networks are built by many individuals over the course of months
and will grow to over 20,000 tasks and 40,000 constraints. I know
that when new tasks are added, redundant constraints are seldom
removed.
If I add a task 4 that should occur between tasks 2 and 3, the network
could be redrawn to look like this:
---------
/
1-----2-----4-----3
and the table would now be:
PE SE TYP
1
2
3
1 2 FS
2 3 FS
4 <---New
2 4 FS <---New
4 3 FS <---New
The constraint
2 3 FS is now redundant since I can get from 2 to 3 via 4.
What would be the best approach to identify the reduntant constraints
in a network and the constraints that make them redundant. For
instance in the above example, I would like to see:
Redundant Made Redundant
Constraint By
------------- -------------
PE SE TYP PE SE TYP
2 3 FS 2 4 FS
4 3 FS
Phil B.
===
Subject: Searching for transient heat-transfers-algorithm for fem
Does anyone knows any good algorithmd for automatic time-integration in
transient heat-transfers-calculations for the finite element method.
The choose of the timestep must be implicit.
I cannot find any good literature about this theme.
Kim Kulling
--
Kim Kulling
email : kim.kulling@web.de
HP : http://www.sir-kimmi.de
===
Subject: Simple matrix problem
I'm trying to find a matrix W so W*A=G where
G is [1 0 0 0; 0 0 0 0; 0 0 1 0; 0 0 0 0] (or some other
non-full rank matrix).
To find W, I can use W=G*inv(A) (1)
or W=pinv(A*pinv(G)) (2).
(1) works generally fine but my problem is that I do not
want to invert matrix A.
Therefore, I came up with (2), however the min-norm solution
W then does not always end up satisfying W*A=G.
How can I find a W without inverting A ? Are there any other
possibilites ? Any help will be appreciated.
===
Subject: something similar to fmincon in shared world?
I am looking in to switching to a Linux platform.
Alas, I rely on Matlab's optimization toolbox and
do not have resources for buying Linux version.
Is there a reasonable facsimile of fmincon() that runs under Linux?
(fmincon is optimization function that handles nonlinear objective and
constraints.)
Julian
===
Subject: Re: something similar to fmincon in shared world?
> I am looking in to switching to a Linux platform.
> Alas, I rely on Matlab's optimization toolbox and
> do not have resources for buying Linux version.
> Is there a reasonable facsimile of fmincon() that runs under Linux?
> (fmincon is optimization function that handles nonlinear objective and
> constraints.)
> Julian
Did you look at octave, mupad or scilab? Well I don't know what exactly
they
have, but its a good point to start. If you have the SuSE distro, these
should come with your linux.
Michael
--
Remove the sport from my address to obtain email
www.enertex.de - Innovative Systeml.9asungen der Energie- und
Elektrotechnik