Re: [eigen] cache-friendly matrix inverse

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

It's actually something I never considered before: for me, as a
mathematician, matrix inversion is a basic operation that "of course"
i consider important, without even asking myself why; if you ask about
practical uses for it, well I'm pretty sure that there must be
situations where you want to solve Ax=b for a single given matrix A,
but for a lot of vectors b and you don't know in advance what these
vectors b will be, you just want to be able to solve very fast
whenever they show up; then the best thing you can do is to precompute
A^-1 so you only have a matrix-vector product to compute whenever a
"b" vector shows up.

Cheers,
Benoit

2009/5/13, Christian Mayer <mail@xxxxxxxxxxxxxxxxx>:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA256
>
> Robert Lupton the Good schrieb:
>> I'm not sure that this is still on-topic, but if you have a model
>> [...] least-squares estimate [...]
>>
>> So you really need to invert a matrix.  You can invert it any
>> way you like (e.g. eigen-value decomposition; Gaussian elimination; ...)
>> but invert it you must.
>
> Well, I knew that you don't need to calculate an explicit inverse there
> (it would have surprised me that such a standard task would invalidate
> the no-inversion-in-numerics rule).
>
> You need a SVD in this case. Anyway, as soon as you've got a numerical
> task to solve, it's allways a good idea to have a look at the numerical
> recepies book, in this case Chapter 15.4:
>
>     http://www.fizyka.umk.pl/nrbook/c15-4.pdf
>
>
> This leaves the question unanswered if these few posts are off-topic?
> I guess: no. It's just a discussion about a usecase of Eigen ;)
>
> CU,
> Chris
>
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.4.9 (GNU/Linux)
>
> iEYEAREIAAYFAkoLJ1cACgkQoWM1JLkHou1b+QCdGqYpzy+lzgEaUg08qme8sh4J
> aD4An3mJB0O53bspef1WSYVCLRmNvUHQ
> =oDBM
> -----END PGP SIGNATURE-----
>
>
>