Here are a couple of quick references, from the R docs and Google
http://www.netlib.org/lapack/lug/node69.html (QR decomp)
http://www.mathcs.duq.edu/larget/math496/qr.html (QR decomp and regression)
The problem with numerics is that accuracy tests can only show problems --
i.e., if you find an example that shows your algorithm performing poorly, you
know you have a problem; but if all of your test cases show good accuracy that
does not mean the algorithm is numerically sound. That's why numerical
analysis exists and why what we tend to do in [math] is to look at the relevant
numerical analysis literature (in this case numerical linear algebra) and what
other packages do when choosing an algorithm. Then, since another wonderful
feature of numerics is that it is almost always true that there is not one
"best" algorithm for all cases, we try to make the implementation pluggable.
I agree with Kim that we can probably grab the QR decomp algorithm from JAMA
(have not looked recently, but I vaguely recall it being there). I will work
on making sure that this does not present any copyright problems. Any
suggestions / straw men for what the interface should look like?
Phil
-----Original Message-----
From: Tzvika Barenholz [mailto:[EMAIL PROTECTED]
Sent: Mon 1/10/2005 9:34 AM
To: Jakarta Commons Developers List
Cc:
Subject: Re: [commons - math] Vector and Scalar multiplications
> The formulas that you cite look correct mathematically, but
> unfortunately not the best numerically. The reference in the post
above
> describes a better computational approach. Patches to support QR
> decomposition of real matrices so we can implement that algorithm or
> other numerically sound multiple regression approaches would be
appreciated.
>
> Phil
not to sound too dumb, but does anyone have a good reference on what
this QR decomposition actually is? I'd love to look at it.
By the way, i've written some tests for my own RealMatrix-based
implementation of multiple linear regression, and the numerics aren't
too bad at all as far as i could tell (first differences appearing
around the 12th digit after the decimal point or so). that is, without
a more comprehensive test. Do you guys maybe have a requirement for
how accurate an algorithm must be to be acceptable?
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