Numerical Analysis

Archive for June, 2010

Merging Standard Deviation

I wanted to know if this is possible.
Suppose I have two sets of numbers

I calculate the mean and standard deviation on set 1.
I then calculate the mean and standard deviation on set 2.

Is there a way of using the standard deviation calculated from set 1
and set 2 to get the standard deviation of the total set ? That is
(total set = set1 + set2) ?

.
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Normal distribution function with skew and kurtosis

The probability density function for the normal distribution with mean ‘m’
and standard deviation ‘s’ is:

   1/(s*sqrt(2*Pi)) * exp(-(X-m)^2 / 2s^2)

How can this formula be generalized to include skew and kurtosis?


Phil Sherrod
(phil.sherrod ‘at’ sandh.com)
http://www.dtreg.com
http://www.nlreg.com

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jordan decomposition and irrational eigenvalues

i have been studying the jordan decomposition lately and from its
algorithmic implementation (filipov’s method), then realised that there may
be computational difficulties arising if any of the eigenvalues are repeat
and irrational.

the case could arise whereby the computer could decide that the repeat roots
are close together rather than repeated irrationals.  also as the
implementation is numerical rather than symbolic, then in the case of an
irrational eigenvalue occurring it would have to truncate its value at some
point, which in turn would affect the solution to
(A – lambdaI)^k x = 0   .

how are these difficulties resolved?  i know mathematica carries out the
jordan decomposition symbolically, but what about numerical implementations?

thanks

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nonlinear, volumetric locking-free H1 element codes?

I’d like to test and use some nonlinear hexahedral locking-free elements within my own software which is currently limited to linear and locking nonlinear elements. Hopefully this doesn’t sound lazy, but if anyone is aware or in posession of element code that I could reuse (absolutely noncommercial, rather exclusively for myself) I’d appreciate if he would share that information with me. It would save me quite significant efforts. My interest regards SRI-, Fbar-, EAS-elements alike, stabilized oder not.

Aditionally, as there are some distinguished experts around here I might be allowed a very general question: for structural hyperelasticity (also in the compressional range) – which robust hexahedral element formulation would you consider the most efficient one?

Thanks you for any input,
Ben

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Quadratic Eigenvalue problems

Hello Friends,
I am going to write my thesis on comparision of different methods on
quadratic eigenvalue problem. can anyone help me in this  regard;
sending me materials,giving suggestions.
my email:roshy…@googlemail.com
best regards

Nab

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Help Decoding A Google Challenge

The moderators of the Google Problems support group post in encrypted
messages that you can’t search through, or even begin to read without
opening the messages.  But once you open them they are decrypted.  So
we have both the encrypted and decrypted messages, and should be able
to find correspondences between the two using some pattern recognition
that’s built into mathematica.  I’ve done this kind of work before, and
the codes are usually 1 to 1, and it isn’t hard if you know how.

Once we figure out the code we can run some other searches, because
I’ve seen another message on the google problems support channel that
end in "–" like all of these codes do, but they were in English.  When
I searched for that phrase the only hit I found was for the song "Round
About Midnight".  So now I am trying to find a way to search for all
refrences on google that are that phrase in code, because you can’t
search for the coded messages unless you can write in the code.

ty

U2VudCEK —
Sent!

U2VudC4K —
Sent.

V2UgaGF2ZSBzZW50IG9uZSB0byB5b3UgYW5kIHNlZSBpZiBpdCB3b3Jrcy4K —
We have sent one to you and see if it works.

QXJlIHlvdSByZXF1ZXN0aW5nIGFuIGludml0ZT8K —
Are you requesting an invite?

V2UgaGF2ZSBzZW50IG9uZSB0byB5b3UgYW5kIHNlZSBpZiBpdCB3b3Jrcy4K —
We have sent one to you and see if it works.

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Linear Algebra problem

Hi i have a problem in one derivation. please go through this and help
me.

A and B are vectors

Here || = norm

if e1 = || A ||   and   e2 = || A + B ||
        1) e1  =   || A||
                 =   || A + B – B||
                <= || A + B|| + || -B ||
                <= || A + B|| + || B ||
                <=  e2 + || B ||
        2) e2  =  || A + B||
                <= || A || + || B ||
                <= e1 + || B ||

Both results are different. I am not able to find mistake in it. Please
help me.

Thanking you

Shailesh Patel

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Re: Simpson Integration – a specific problem

On 11 Jun 2006 02:35:00 -0700, "MET" <Marcel.E.Tschu…@gmail.com>
wrote:

The correct place for this is sci.math.num-analysis.

- Hide quoted text — Show quoted text -

>Normally Simpson is used for integrating between an interval a to b, by
>using the end points of the interval (a and b) as nodes. An advantage
>of this procedure is, that by doubling the number of nodes between two
>iteration loops the already calculated nodes can be reused, so that
>only about half of the nodes have to be calculated new.
>Due to a singularity at one of the end points of the interval, I try to
>apply the Simpson integration slightly different. I split the
>integration interval a to b in in equidistant subintervals and use the
>middle of these intervals as nodes. If, in this procedure, the number
>of nodes would be doubled one would loos the possibility of reusing
>already calculated nodes. This disadvantage can be overcame by trebling
>the number of nodes from one iteration loop to the next, i.e. in an
>iteration loop one third of the nodes can be used from the previous
>loop and two thirds have to be calculated new. This adjusted procedure
>calculates the integral, but, contrary of what I would have expected,
>with a very poor "efficiency".

>Comparing the required number of iteration loops for a given
>Rel. Error = ABS( 1 – Result_new_Loop / Result_old_Loop )
>between the adjusted Simpson procedure and a "basic" numerical
>integration (sums of Fi*dF, doubling nodes without reusing already
>calculated ones) shows the following differences:

>Adjusted Simpson Procedure:
>Rel. Error   Result   Number of nodes
><1E-3     2062.2593       78732
><1E-4     2063.7296     4960116
><1E-5     2063.8892   389014812

>"Basic" iteration procedure
>Rel. Error   Result   Number of nodes
><1E-5     2063.9027        3072 (approx. * 2)
><1E-8     2063.9091      294912 (approx. * 2)

>Questions:
>I can somehow understand that the adjusted Simpson procedure requires
>more iteration loops since the relative error is calculated with twice
>the number of "new" nodes compared to the number of "old" nodes. But
>why is the result not more accurate with the much larger number of
>nodes? Or, are the Simpson factors for the sums (1, 4 and 2) not the
>same for this adjusted version? Is there a possibility to adjust the
>Simpson integration so that it becomes more efficient than the "basic"
>iteration procedure?

>Thank you for your help.

>Marcel

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recommended books on rigorous numerical methods

Dear group,

After going through some previous posts discussing various books on
numerical analysis and/or numerical methods, I dare to give it another go.

As a physics pre-graduate I have been using Numerical Recipes by Press
et. al. up till recently. For various reasons, I’m not satisfied with
this title. What I would ideally like to obtain is a book

(*) treating "standard" numerical methods (which for me would include
interpolation, function evaluation, linear systems/eigenproblems, root
finding, quadrature, initial values problems for ode, discussion of
stiffness)

(*) containing no code (not in the book, not referring to a cd) but
being sufficiently algorithmically oriented to enable the reader to
write his own routines after reading. I like writing the code myself.

(*) practical but still rigorous on its discussion of algorithms,
applicability, error etc. (As opposed, in my view, to NR.)

A First Course in Numerical Analysis by Ralston et. al. came to my
attention. Given the above, would it be a good choice or is it dated?
Other (better) alternatives?

Opinions are appreciated!

Kind regards,
Gerard.

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THE MATRIX IS PERFECT MORE COMPLEX THEN THE UNIVERSE and if you took a

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