Newsgroups: comp.lang.apl
Path: watmath!watserv2.uwaterloo.ca!torn!utcsri!torsqnt!jtsv16!itcyyz!yrloc!hui
From: hui@yrloc.ipsa.reuter.COM (Roger Hui)
Subject: Re: Numerical Analysis + APL/J
Message-ID: <1992Aug11.043206.9360@yrloc.ipsa.reuter.COM>
Organization: Iverson Software Inc.
References: <BEVAN.92Aug3165658@jaguar.cs.man.ac.uk> <1992Aug6.033157.6833@yrloc.ipsa.reuter.COM> <1155@kepler1.rentec.com>
Date: Tue, 11 Aug 92 04:32:06 GMT

Andrew Mullhaupt writes:
 
> For Householder QR, all the matrix multiplications should be carried out by
> rank-1 updates, which are O(N^2), not O(N^3). Divide and conquer doesn't
> speed this up at all, so the complexity of the QR is not affected by the
> use of the Strassen trick. In fact, this kind of update is actually one of
> the things which is relatively fast in APL, so the constant term in the O(N^2)
> is pretty good. Since you have to do N^2 work to produce the output of the
> matrix multiplication, the usual approach of rank-1 updates is close to
> optimal.
 
My msg said, "QR applies to a real or complex matrix A with linearly-
independent columns and returns an Hermitian matrix Q and an upper
triangular matrix R, individually boxed, such that A = Q +/ .* R."
I would be quite surprised if this can be done in O(n^2) time.

------------------------------------
Roger Hui, Iverson Software Inc., 33 Major Street, Toronto, Ontario  M5S 2K9
Phone: (416) 925 6096;  Fax: (416) 488 7559
