Newsgroups: comp.lang.apl
Path: watmath!watserv2.uwaterloo.ca!torn!cs.utexas.edu!sdd.hp.com!wupost!uunet!s5!sethb
From: sethb@fid.morgan.com (Seth Breidbart)
Subject: Re: Numerical Analysis + APL/J
Message-ID: <1992Aug17.165305.2364@fid.morgan.com>
Organization: Morgan Stanley & Co., New York, NY
References: <1169@kepler1.rentec.com> <1992Aug14.032619.16083@yrloc.ipsa.reuter.COM> <1177@kepler1.rentec.com>
Date: Mon, 17 Aug 1992 16:53:05 GMT
Lines: 16

In article <1177@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>In article <1992Aug14.032619.16083@yrloc.ipsa.reuter.COM> hui@yrloc.ipsa.reuter.COM (Roger Hui) writes:
>
>>[Aside:  You say, "It can't".  I believe it would be quite difficult to
>>prove that QR can't be done in time O(n^2) (or O(m*n) on an (m,n) matrix).]
>
>How about an oracle argument. Suppose you guess Q and R in O(1). You
>have to then verify it by checking that R is upper triangular, 
>and then you must verify that Q is (column) orthogonal. You don't have
>to check the lower triangle of QTQ, but this leaves O(n^2) things to check.

I can generate the "group operation matrix" for the integers mod n
under addition in time n^2; you can't check an arbitrary nxn matrix to
see if it's a group that fast.

Seth		sethb@fid.morgan.com
