Re: [eigen] inverse() method for TriangularView class? |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] inverse() method for TriangularView class?*From*: Douglas Bates <bates@xxxxxxxxxxxxx>*Date*: Mon, 31 Oct 2011 14:22:08 -0500*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=mime-version:sender:in-reply-to:references:date :x-google-sender-auth:message-id:subject:from:to:content-type :content-transfer-encoding; bh=7cWGA39QAkttrnor9dNHEWjxkAtzNX9cCqbw1F0A8CU=; b=AGgQ+fUgaeeLwr851qd0UBnhQBhtgpibUu110q87sS/Hk7Gj1Tj7610Bj98Ipa9qIv HVToc1I/gKa2w9Zeg7hpuw36evg2uaicwFXacENTsc6CiCwGKTxyDcGOuGy/RSUthciJ NTUCrY/lW+s4o6BGXPlzSMSNLZWcMTMcZR0gg=

On Mon, Oct 31, 2011 at 1:46 PM, Helmut Jarausch <jarausch@xxxxxxxxxxxxxxxxxxx> wrote: > On 10/31/2011 06:10:16 PM, Douglas Bates wrote: >> In my case it is not that I want to use the inverse to form solutions >> of systems. I actually want the inverse and at present am applying >> solve to the identity matrix to obtain it. My proposal for an >> inverse >> method is simply to make my code more concise and transparent. >> >> A common operation in statistical computing is solving a least >> squares >> problem, $\hat{\beta}=\arg\min_{\beta}\|y - X\beta\|$ and calculating >> the standard errors of the estimated coefficients. That calculation >> requires the square roots of the diagonal elements of X'X. If you > > Isn't it more stable to use the SVD of X = U S V' (S diagonal) > Then (X'X)^(-1)= V S^(-2) V' You can use the SVD but, depending on the size of the model matrix, X, the SVD can be much, much slower than using a LDLT decomposition of X'X. The latter method does involve calculating X'X whose condition number is the square of the condition number of X, which is a disadvantage. But even if you don't want to form X'X you could use a column-pivoted QR decomposition to get close to the speed of the Choleksy decomposition. And both are much faster than the SVD on large examples.

**References**:**[eigen] inverse() method for TriangularView class?***From:*Douglas Bates

**Re: [eigen] inverse() method for TriangularView class?***From:*Benoit Jacob

**Re: [eigen] inverse() method for TriangularView class?***From:*Douglas Bates

**Re: [eigen] inverse() method for TriangularView class?***From:*Helmut Jarausch

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