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I correct my typos . please read again...

aminer

5/21/2014 11:33:00 PM

I correct my typos . please read again...

Hello...


I have come to an interresting subject...


As you have noticed i have implemented a parallel conjugate gradient
solver, here it is:

https://sites.google.com/site/aminer68/parallel-implementation-of-conjugate-gradient-linear-sys...


This parallel solver is useful in mathematical finit elements
calculations etc.

but it is also useful in mathematical calculations of Markov chains...


Mathematical eigenvectors shows in phemenons that exhibit a stable
behavior with time... and in Markov chains we searh also for
an eigenvector where the systeme will stabilize so we have to resolve:

A*vector(v) = 1*vector(v)

A is the transition matrix
and v a vector.


So since the Eigenvalue is 1 that means we have to solve the
following system of equationa that will give you the eigenvector
where the system will stabilize its behavior:

(A - I)*vector(x)= vector(0)

I is the indentity matrix.

And you can solve this system of equations by
my parallel conjugate gradient system solver also..

or you can solve the following system of equations:
(Transpose(A) - I)*vector(x)= vector(0)


And you can solve this system of equations by
my parallel conjugate gradient system solver also..



Thank you,
Amine Moulay Ramdane.