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Subject: Re: how to deal with the inversion problem of a huge sparse
Date: Sun, 27 Sep 2009 18:37:04 +0000 (UTC)
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <h9oai6$o47$1@fred.mathworks.com>...
> Rune Allnor <allnor@tele.ntnu.no> wrote in message <ef773a28-76ca-4e60-b6ee-dc944f4e6ba0@h30g2000vbr.googlegroups.com>...
> 
> > 
> > Again, any desire to invert a large matrix is almost always
> > wrong.
> 
> Finite element methods, solid mechanics, thermal calculation, fluid dynamic, seismic inversion, statistics, data mining, machine learning, data assimilation, weather forecast, quantum mechanics simulation, image reconstruction in medical, photogrammetry, etc... all often call for inversion of huge system of linear equations. As far as I know they all seem to work alright.
> 
> Bruno

Do these problems call for the inversion of a large matrix? Or do they simply call for the solution of a set of large (and almost always sparse) set of linear equations?

The latter does NOT imply a need for the former. Thus the statement "any desire to invert a large matrix is almost always wrong" is true.

One might write an analytic solution using the inverse of a matrix, but that does not imply that the inverse is the only or even preferred way to numerically compute a solution. The way equations are written on paper or in a text book are almost never the way they are solved on a computer if the problem size is sufficiently large.

FWIW

Duane

Duane