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From luc <...@spaceroots.org>
Subject Re: [math] refactoring least squares
Date Tue, 25 Feb 2014 16:39:28 GMT
Hi Ted,

Le 2014-02-25 15:42, Ted Dunning a écrit :
> On Tue, Feb 25, 2014 at 6:22 AM, Konstantin Berlin 
> <kberlin@gmail.com>wrote:
> 
>> Hi,
>> 
>> I am really having problems believing that matrix copying is the major
>> problem in an optimization algorithm. Copying is O(N^2) operations. 
>> Surely,
>> for any problem where performance would matter, it is completely 
>> dwarfed by
>> the O(N^3) complexity of actually solving the normal equation.
>> 
>> Also, I think testing should be done on an actual large problem where
>> scaling issuing would show up. The 1000x2 jaccobian would results in a 
>> 2x2
>> normal equation. Surely this is not a good test case.
>> 
>> Konstantin
>> 
> 
> As you point out, the test case in question shows how copying dominates
> computation for massively over-determined systems.

You are right. Massively over-determined systems is also an important 
class of problems,
so it needs to be addressed. I am aware there are many other important 
classes of
problems, though, so there are probably no silver bullets and what is 
important here
is not important elsewhere. There are also cases for which forming the 
normal equations
is avoided (mainly for the sake of numerical robustness if I remember 
correctly), so
once again no silver bullets.

best regards,
Luc

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