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Re: Large array memory problem. [message #46458 is a reply to message #46412]

Wed, 23 November 2005 12:43

Marius Hagen
Messages: 3
Registered: November 2005

Junior Member

Carolina wrote:
> Does anyone know a clever trick to compute inverse of large sparse
> matrices?

While I'm no expert on the subject, I do spend a lot of time working
with large matrices, so maybe I can say a few things that might help
here. In most instances getting the inverse of a large matrix is a *bad
idea*, since, in floating-point math, you can easily wind up amplifying
very small errors in the input into HUGE errors in the output. For an
array with 10^8 elements, even in double-precision, most direct matrix
inverses are so corrupted with these amplified errors as to be almost
useless. Instead, what most people try is to use either a direct solver
or an indirect solver of the *forward* matrix problem.

That is, if you are trying to calculate Ax = b (A=huge matrix, x and b
long vectors), then rather than solving this as x = A^-1 b, you can use
QR decomposition to change the form of A such that it is easy to solve
by back-substitution. This can be rather slow, so an alternative is to
obtain an approximate solution for x by use of an iterative solver.
These are much faster, and typically they can obtain as much accuracy
as you want in a fraction of the time that a direct solver requires.
And these techniques do not have the extreme amplification of small
errors.

Having said that, my own work is entirely in matrices which do not have
an inverse at all, and which have 10^15 elements or so, and so
iterative solvers are my only choice. Choosing which algorithm to use
here is an art --- generally each application wants something
different. But if you have access to Matlab, its support for sparse
matrix routines and for direct or indirect matrix solvers is
impressive.

- Marius

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[Message index]

		Large array memory problem. By: Pitufa on Tue, 22 November 2005 04:39
		Re: Large array memory problem. By: Marius Hagen on Wed, 23 November 2005 12:43
		Re: Large array memory problem. By: news.qwest.net on Wed, 23 November 2005 11:19
		Re: Large array memory problem. By: Pitufa on Wed, 23 November 2005 10:12
		Re: Large array memory problem. By: Marius Hagen on Tue, 22 November 2005 14:16
		Re: Large array memory problem. By: Nigel Wade on Mon, 28 November 2005 03:40

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