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From: Bruno Luong on 7 Jul 2010 17:11
"Lukas " <lukas.bystricky(a)afcc-auto.com> wrote in message <i12pfg$dnd$1(a)fred.mathworks.com>...
> "Steven Lord" <slord(a)mathworks.com> wrote in message <i12jo4$13k$1(a)fred.mathworks.com>...
>
> > Well, there is one other thing you could try. Most if not all of the sparse
> > iterative solvers accept either a sparse matrix A or a function that given x
> > computes A*x and/or A'*x.
> >
> > http://www.mathworks.com/access/helpdesk/help/techdoc/ref/f16-5872.html#f16-6565
> >
> > If you can perform this matrix-vector multiplication efficiently using the
> > "packed" form of your matrix, you may be able to solve the problem without
> > having to create the full or sparse A matrix.
> >
> > --
> > Steve Lord
> > slord(a)mathworks.com
> > comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
> > To contact Technical Support use the Contact Us link on
> > http://www.mathworks.com
> >
>
> Steve,
>
> I'm not sure I understand. Could you be more specific? I can't really see any of the functions being overly efficient on banded matrices. Also is reduced accuracy a concern with any of these methods?
>

Steve refers to iterative methods to solve A*x = b where users must provide a *function* that performs the matrix*vector product A*z for a given z (as opposed to providing explicitly the matrix value A). In this case, you are responsible to exploit the band characteristic of your matrix so as to carry out the product in the most efficient way. This technique is used mostly in PDE where the matrix is built by discretizing of a local differential operators, thus very sparse.

Bruno
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