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From: dik@cwi.nl (Dik T. Winter)
Newsgroups: comp.arch
Subject: Re: massive linpack
Message-ID: <3654@charon.cwi.nl>
Date: 9 Jun 91 01:42:40 GMT
References: <9106080254.AA12624@ucbvax.Berkeley.EDU>
Sender: news@cwi.nl
Organization: CWI, Amsterdam
Lines: 36

(It would simplify matters a bit if you clearly distinguish what you quote and
what you write yourself.  On occasion your answer comes immediately after a
quoted paragraph, but you insert a blank line when quoting multiple paragraphs.
Is that correct?)

In article <9106080254.AA12624@ucbvax.Berkeley.EDU> jbs@WATSON.IBM.COM writes:
 >                   I suspect that the worst case bounds on error
 > estimation were not satisfactory.
They are reasonable if you do backward error analysis, they tend to be very
bad when doing forward error analysis.

 >                                  If this does not happen then you are
 > certain to be ok. This problem is almost never seen in practice.  There-
 > fore my statement about typical behavior.
This is again considering backward error analysis.  Yes, most numerical
algebra literature is concerned with the backward analysis.

 >           QR and SVD are used for solving least squares problems.
SVD is a very good tool to solve a set of linear equations if:
1.  the condition number is large.
2.  the matrix is too large to be stored in memory.
There may be more reasons.

 >                                                                    Least
 > squares problems can be formulated as linear equations (the normal equa-
 > tions) but doing so unnecessarily increases the condition number.
True, the condition number is squared.

 >           As to credibility:
If you want my credibility:

I have been working in numerical algebra since 1968.
Linear equations, eigenvalues, singular value decomposition etc.
--
dik t. winter, cwi, amsterdam, nederland
dik@cwi.nl