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Author: Robert IsraelRobert Israel
Date: Jan 18, 2007 20:23
In article newssvr29.news.prodigy.net>,
Calvin Guan nospam.broadcom.com> wrote:>Hello,
>
>I'm trying to convert an 2nd order ODE to difference equation
>and solve it
>numerically. Here is an example.
>
>y''=sin(x), given the IC y(0)=0 and BC y(3.14)=0. This can be solved
>analytically if y'(0) is known.
>
>I convert the ODE to DE like:
>
>y(n+1)-2y(n)+y(n-1)=h*h*sin(n*h)
>
>given initial value y(0)=0
>and final y(m+1)=0 where h=3.14/(m+1)
>
>This can be solved by constructing a m*m matrix. but it became
>very resource ...
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Author: Peter SpellucciPeter Spellucci
Date: Jan 18, 2007 09:28
>
>David Jones wrote:
>> Madhu wrote:
>>>
>>> The user types each entry for just the lower triangular matrix of R
>>> (since R is Hermitian) through a GUI.
>>>
>>
>> An obvious question is why? Where is the user supposed to get this
>> matrix R from? If users are just setting up example problems, then
>> they are likely to find it easier to work in a manner where they
>> themselves supply the elements of decomposition matrix (not
>> necesariliy a Cholesky decomposition): ie they can think of their
>> random vector K as K=AZ, where Z's are uncorrelated etc. and the user
>> would supply A directly.
>
>Thanks for your response David.
> ...
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Author: Tim vor der BrückTim vor der Brück
Date: Jan 17, 2007 07:11
Does someone knows a good free! C software for linear optimization?
Thank you for any help
T.
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Author: MadhuMadhu
Date: Jan 16, 2007 12:58
I am developing an application that takes a correlation matrix (R) as
its input. R is a Hermitian matrix that has the correlations between a
set of complex Gaussian random variables.
If K is a matrix that has a set of complex Gaussian random variables, R
is defined as R=E(vec(K)*vec(K)^H), where K^H is hermitian of vec(K)
So R is a matrix of complex random variables.
Other properties of the matrices:
->entries of K are complex normal, (have 0 mean and unit variance)
->main diagonal entries of R are unity
The user types each entry for just the lower triangular matrix of R
(since R is Hermitian) through a GUI.
I need to ensure that the matrix R is positive definite. This is
because the R matrix is positive definite and I will be doing a
Cholesky decomposition on it.
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Author: Peter SpellucciPeter Spellucci
Date: Jan 16, 2007 09:59
>Hi,
>
>In Bronstein/Semendjajew/Musio/M=FChlig (2000), Taschenbuch der
>Mathematik, p. 891, it is stated that the following algorithm can be
>used to find the minimum x* of the problem f(x) =3D min!, x \in R^n:
>
>1) Set x =3D x^1, where x_1 is some appropriate approximation for x*
>
>2) Solve for r=3D1,2,...,n the one-dimensional optimization problems
>
> g(a_r) =3D f(x_1^(k+1), ..., x_{r-1}^{k+1} + a_r,
||| either a "," here
or x_r^k instead of x_{r-1}^{k+1}
what is intended: minimization with respect to the r-th coordinate
>x_{r+1}^k,...,x_n^k) =3D min!, a_r \in R^n
>
> If a_r is a minimum or an approximation to the minimum of the r-th
>problem, set x_r^{k+1} =3D x_r^k + a_r. ...
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Author: mecej4mecej4
Date: Jan 16, 2007 08:54
Stig Holmquist wrote:
> The most common bell shaped curve is the normal or Gaussian but
> not all data forming a symmetrical bell shaped curve are normal.
>
> I wen to Google to search for other bell curves but found none.
> Is there a book discussing other bell curves and how to find
> their standard deviation from the mean?
Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory,
Oxford Univ. Press, ISBN 0 340 61430 7
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Author: Stig HolmquistStig Holmquist
Date: Jan 15, 2007 17:01
I would like to generate a normal curve with mean=150 and
standard deviation=32.8 with a range from 21 to 279.
Can this be done with Excel, and if so, how should I do it?
Stig Holmquist
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Author: DiabofloDiaboflo
Date: Jan 15, 2007 06:37
Hi,
I have a quite large system of linear equations to solve (Ax=b). For my
simulations this step has to be done several hundred times for similar
matrices. The matrix is quite empty (most elements = 0) and I could
separate this problems into a few smaller matrices which would reduce
the number of elements (eliminate all elements = 0).
To solve the problem I use the NAG function f04adf which solves the
system as followed:
Given a set of complex linear equations AX = B, the routine first
computes an LU factorization of A with
partial pivoting, PA = LU, where P is a permutation matrix, L is lower
triangular and U is unit upper
triangular. The columns x of the solution X are found by forward and
backward substitution in Ly = Pb
and Ux = y, where b is a column of the right-hand side matrix B.
Do I save calculation time by splitting up the problem into many small
ones? Is there a way to find out how remarkable the difference is?
Thanks,
Florian
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