On 9 Sep 2009, at 15:18, Arnold Neumaier wrote:
John Pryce schrieb:
I seem to be suffering mental exhaustion with all the ideas flying
round, so I would appreciate a summary of the interval Newton method
(esp. the multivariate case) showing how and where both the interval
and the decoration are needed. It sounds as if it falls into the
category I named B3 in my email of 8th Sept.
If F is continuous on X and F(X) in X then the intersection of F(X)
and X contains a zero of X. Clearly, both the interval and the
decoration are needed here.
Why? One needs either F(X), or the knowledge that F may not be (defined
and continuous) on X, but not both at once. That is, if
"possiblyUndefined" is raised you don't need F(X) so you can overwrite
it with a value that denotes "possiblyUndefined". This seems like my
case B1, not B3.