inconsistent condition numbers from cond, det, inv functions

[Rolf Fabian]

Forgot to mention my conclusions about the subject title:

Because ML seems to use (2 times) 2-norm for cond() by default
(if input is regular) as also does Octave, we shouldn't change
the cond() default in order to conform to ML. Unfortunately
this default uses the slowest flavour of norm (even two times).

But as soon as cond() accepts also a 2nd (p) input, everbody is
free to speed it up for larger matrices by using p=1 or p=Inf or 'Inf'
or even 'fro'.

Reciprocal condition number rcond from 2nd output of
det() and inv() are obviously determined via 1-norm which is
much faster than 2-norm. One might discuss whether 'inf' or 'fro'
might be a better choice than 1-norm. But this is off-topic at the
moment. Somebody should fix help parts of  det() and
inv() by cleary specifying that 1-norm reciprocal condition number
is used in order to prevent further confusion.

IMHO the help part of 'cond' also needs to be fixed because
usually mathematicians do not use 'two-norm' while
refering to '2-norm'.

Rolf Fabian






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Rolf Fabian
<r dot fabian at jacobs-university dot de>

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