comp.programming

aminer

5/21/2014 11:13:00 PM

On 5/21/2014 4:07 PM, aminer wrote:
>
> Hello,
>
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> I have come to an interresting subject...
>
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> 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...
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> This parallel solver is useful in mathematical finite elements
> calculations etc.
>
> but it is also useful in mathematical calculations of Markov chains...
>
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> 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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