Mathematica, ARPACK and implicit matrices
- To: mathgroup at smc.vnet.net
- Subject: [mg96562] Mathematica, ARPACK and implicit matrices
- From: Fernando Cucchietti <Fernando.Cucchietti at icfo.es>
- Date: Mon, 16 Feb 2009 06:59:21 -0500 (EST)
- References: <firstname.lastname@example.org> <4997A3D9.email@example.com>
I am trying to find the largest eigenvalue and associated eigenvector
of a very large matrix, mildly sparse but without a simple structure
-- that is, zero elements are arranged in a seemingly random way.
Mathematica uses ARPACK routines for this task. However, it appears
that it wants to construct the matrix explicitly before starting. This
is strange when compared to how ARPACK works, and in fact it is the
one thing I was trying to avoid doing: Writing down the matrix takes
too much memory and time, even if it is sparse.
ARPACK is designed to require not the matrix, but just a function that
gives the result of multiplying the matrix with an arbitrary vector. I
call this an implicit definition of the matrix, hence the subject of
the email. This would work very well with me since I have a compact
expression of the matrix in the form of a function that returns the
product with a vector, and I would not need to define the array
I have been looking but I cannot find an option or a way to make
Mathematica give me the eigenvalues without writing the matrix
explicitly, any suggestions?
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