Re: [eigen] cache-friendly matrix inverse |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] cache-friendly matrix inverse*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Wed, 13 May 2009 22:10:40 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=qllIodeJGp5Z8EVJw3VNf0sydkjTmWyC0TGc0PyHA+U=; b=GcU9kEWpqPX09cj/6ToXFnrCodNxoCcdxeMO4obFHW/Y701SPbJOy3MffxR3iF6joU Xw3/bA3hC+wP+zUnSCb46dNmNkw3nKm9nZvXhLuZD10jGnk/y1gm5nzXZUkMguVROJyd P058YU5tItHQ6kDwpO9V9i6DWwf8v8XGDABwo=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=AFett4K0tDGIzXi1YIFNx/2rWASt3mmflGcq9ebSycJnn6gQw/qU6LBiSJeyE6f83O zPmcQ2bY01skT45vNCP2y/AVAeDaxZCtD1BKsCNG2DO5NAPL0yTd4O3+eCDK95uQxC7N 9N8W1aaV+E41xEMRyl7yMudQx4tdyn9fbd1tY=

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----- > > >

**Follow-Ups**:**Re: [eigen] cache-friendly matrix inverse***From:*Christian Mayer

**References**:**[eigen] cache-friendly matrix inverse***From:*Benoit Jacob

**Re: [eigen] cache-friendly matrix inverse***From:*Christian Mayer

**Re: [eigen] cache-friendly matrix inverse***From:*Robert Lupton the Good

**Re: [eigen] cache-friendly matrix inverse***From:*Christian Mayer

**Re: [eigen] cache-friendly matrix inverse***From:*Robert Lupton the Good

**Re: [eigen] cache-friendly matrix inverse***From:*Christian Mayer

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