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.
Eugene
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