[Jprogramming] matrix inversion operator

[Roger Hui]

> But I defer to Roger Hui, who is a genuine mathematician -- 

As Ken Iverson had said (http://keiapl.info/anec/#Dickey),
Don't call me a mathematician because it would
offend a real mathematician.



----- Original Message -----
From: Eugene McDonnell <eemcd at mac.com>
Date: Friday, July 6, 2007 14:59
Subject: Re: [Jprogramming] matrix inversion operator
To: Programming forum <programming at jsoftware.com>

> 
> On Jul 6, 2007, at 12:48 AM, Damien wrote:
> 
> > Hello,
> >
> > I was wondering what kind of algorithm is used within the %. 
> operator,> because it is very powerful !! Does someone have any 
> idea ?
> > Besides, what is the best algorithm to invert matrix for you ? 
> I  
> > mean if you
> > had to implement only one algorithm for all the types of 
> matrices,  
> > which one
> > would you choose ?
> >
> > Thanks.
> > Damien.
> 
> A bit of background:  it was 1986. I. P. Sharp Associates 
> had a  
> contract with Hitachi to give them an APL system, with the 
> proviso  
> that Sharp would guarantee that every item delivered to them 
> was  
> orginal, so that no other vendor (STSC, IBM)  could say 
> that their  
> software had been stolen.
> 
> As a consequence, Sharp undertook to write a complete APL system 
> that  
> was completely written from the bottom up. Doug Forkes and 
> I  
> undertook to write the desired software.
> 
> One of the components that I undertook was "Domino", so 
> called  
> because the glyph for matrix inverse was Quad (a rectangle) on 
> which  
> was superimposed the divide glyph. The result looked like a 
> domino  
> tile, so that was what it was called.
> 
> In brief, I used the QR Algorithm (quotient remainder), 
> and  
> Householder Triangularization.
> 
> However, I used devilishly sly ways of doing this, in such a way 
> that  
> I was asked how I was able to get such great speed.
> 
> But I defer to Roger Hui, who is a genuine mathematician -- 
> whereas I  
> spend my time on Jane Austen, Dante, Robert Frost, Navajo 
> Indians and  
> the Aubrey-Maturin series.