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Topic: Sparse linear system
Replies: 14   Last Post: May 21, 2010 9:47 AM

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Posts: 11
Registered: 5/19/10
Re: Sparse linear system
Posted: May 19, 2010 10:22 AM
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On 19 Mag, 12:07, luca <> 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,


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