# [R] underdetermined system

yoooooo magno_yu at ml.com
Tue Oct 16 21:02:11 CEST 2007

```Turns out someone asked this before ;)

http://tolstoy.newcastle.edu.au/R/e2/devel/07/04/2981.html

>
> QR is good for overdetermined LS problems, and I don't think that it can
> be
> used for "minimum norm" solution of underdetrmined LS problems.  You need
> LAPACK's Fortran routine DGELS.  I am not sure if this currently available
> in R.
>
> Ravi.
>
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>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
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>
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On
> Behalf Of yoooooo
> Sent: Tuesday, October 16, 2007 11:34 AM
> To: r-help at r-project.org
> Subject: [R] underdetermined system
>
>
> Hi, sorry, I'm an idiot.. and I know I'm missing something stupid..
>
> I thought if we solve an underdetermine system with QR, my soln is:
>
> min ||x|| (L2 sense)  such that Ax = b
>
> then say i have:
>
>> w <- matrix(c(1, 5), ncol=2)
>> sw = 2
>> qrW = qr(t(w) %*% w)
>> qr.coef(qrW, t(w) %*% sw)
>      [,1]
> [1,]    2
> [2,]   NA
>
> but we also have soln (0, 2/5) which obviously has a smaller distance in
> L2
> than (2, 0). Am I missing something very obvious? Thanks a lot!!!!
>
> - yoooooooooooooooooo
>
>
>
> --
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