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Markov chains...

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  Markov chains... aminer <aminer@toto.net> - 2014-05-21 16:07 -0700
    Re: Markov chains... aminer <aminer@toto.net> - 2014-05-21 16:12 -0700

#2368 — Markov chains...

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-system-solver


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

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


Mathematical eigenvectors shows in phemenons that will 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*vecteur(v) = 1*vecteur(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)*vecteur(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)*vecteur(x)= vector(0)


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



Thank you,
Amine Moulay Ramdane.

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#2369

On 5/21/2014 4:07 PM, aminer wrote:
>
> 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-system-solver
>
>
>
> This parallel solver is useful in mathematical finite elements
> calculations etc.
>
> but it is also useful in mathematical calculations of Markov chains...
>
>
> Mathematical eigenvectors shows in phemenons that will 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*vecteur(v) = 1*vecteur(v)



vecteur in french means vector.



>
> 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)*vecteur(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)*vecteur(x)= vector(0)
>
>
> And you can solve this system of equations by
> my parallel conjugate gradient system solver also..
>
>
>
> Thank you,
> Amine Moulay Ramdane.
>
>
>
>
>
>
>
>
>
>
>
>

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