> 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 <[EMAIL PROTECTED]> Date: Friday, July 6, 2007 14:59 Subject: Re: [Jprogramming] matrix inversion operator To: Programming forum <[email protected]> > > 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. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
