luca
Posts:
11
Registered:
5/19/10
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Re: Sparse linear system
Posted:
May 19, 2010 10:22 AM
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On 19 Mag, 12:07, luca <luca.frammol...@gmail.com> wrote:
> Hi,
>
> suppose i have a matrix M X N of reals. This matrix is sparse. Every
> row has only 3 non zero values (they are always -1, 2, -1). The M and
> N are on the order of 600-800.
>
> Is there a fast library (way) to solve a sparse linear system A X = B,
> where the matrix A is of the type defined below??
>
> I need a library writte in C/C++ that is possibly portable.
>
> Thank you,
> Luca
A is a NxN real sparse symmetric matrix. Sorry for the confusion. I
will give you guys more details. The problem i am facing is the
following. Given a NxN real sparse symmetric matrix A, solve the
following system of linear equation:
(A + aI)X_{t} = aX_{t-1} - grad(F(X_{t-1}))
where <a> is a real scalar (the step size), X_{t} is a vector of N
reals, F is differentiable function, I is the identity matrix.
One start with an arbitrary X_0 and <a> = some constant and every
iteration involves the solution of this system of linear equations and
the update of the scalar <a> using some schedule.
Since A is a big sparse matrix, A+aI is a big sparse matrix too. So i
could use a LU factoriztion of A+aI and than solve
the system in the usual way.
A does not change during the iterations, but the coefficient matrix is
A+aI, so i need to compute the LU of A+aI.
I would really like to avoid the LU factorization at every iteration,
but i don't see any alternative. Maybe there is a way
to compute LU of A and than, given aI, compute (in a fast way) the LU
of A+aI using the LU of A...
So, what i need is a free portable C/C++ code for computing a fast LU
factorization of a sparse matrix.
Thank you,
Luca
So,
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