Re: [eigen] cache-friendly matrix inverse |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] cache-friendly matrix inverse*From*: Christian Mayer <mail@xxxxxxxxxxxxxxxxx>*Date*: Wed, 13 May 2009 22:43:11 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:sender:message-id:date:from :reply-to:user-agent:mime-version:to:subject:references:in-reply-to :x-enigmail-version:content-type:content-transfer-encoding; bh=RBnSKm00UkZs9pYVVUImKjjtrABE5eXk8gvIJXn9/hM=; b=aWy1ARD5tb1RNfmqSUz1SJwZg3NUxLrvh/4JGPww4e3Y0YSaUKtB6eePSuBLTvTBel FEeNZaZKtdJ+Zx4ViShvu9EtIdCgwjyIeWWikIYuIDtCMzZ0Bm3M1Q46JsWy0aW8tLBN AE8Bl+FF9Er/AT9NdovbftwvNRkplqeqh5s0g=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=sender:message-id:date:from:reply-to:user-agent:mime-version:to :subject:references:in-reply-to:x-enigmail-version:content-type :content-transfer-encoding; b=OyITRmnm/lClpC2wd/ZD8IKCyUoGVM4gq22E5BOXwI6fj0Ax91d6Mjs7G2xfpKc+3q f8AhSUGEZX31VIK40Ay166pgvB8BUcGKrRSgwsceBSzfogGsnboMnbiI08uaOcqGgBPf oATzcMv7qyhN03yWRKbFbNN61Ec56ykLRb4nA=

-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA256 Benoit Jacob schrieb: > 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. That's *exacly* what LU decomposition is for. Compute it once and use it to solve the equation many times. Note: the amount of operations to calculate A^-1 and an LU decomposition is the same. *AND* using a LU to solve the equation (foreward and backward substitution) takes also as many operations as a matrix multiplication (i.e. exactly the same as a multiplication with the inverse) An inverse matrix is an extremely usefull "method" in mathematics - as long as you aren't *calculating* it in numerics :) -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) iEYEAREIAAYFAkoLMN4ACgkQoWM1JLkHou2I2wCcDdg3cPH6XhlSoHLu1w4kF2qT wPUAn3ukF0Dr0Qg8g71C4dPXDLEhTyRj =tinR -----END PGP SIGNATURE-----

**Follow-Ups**:**Re: [eigen] cache-friendly matrix inverse***From:*Benoit Jacob

**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

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

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