[R] underdetermined system

[Ravi Varadhan]

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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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

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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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