Re: Potential well and decorations
Dominique:
On 7/7/2011 8:42 AM, Dominique Lohez wrote:
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.
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Be careful.
Before defining such a user-defined function
you must insured that
1) The Interval expression is an straight-forward extension of your intended real expression
2) It satisfies the isotonicity requirement
3) It provides a decoration not best that the expected decoration
Regarding your point 3:
Do you mean the decoration should not be better than the "expected
decoration?" If so, how is the "expected decoration" defined? Presumably
the standard will define unambiguously what the output of a single
operation will be, given its inputs. That would be the
"expected decoration." If by "expected decoration," you mean
the output from a particular expression equivalent to the function
in infinite-precision (i.e. real) arithmetic, that is necessarily
ill-defined. I note that the particular example Dan gave is
defined and smooth (correct me if I missed something) everywhere on
the real line, and it can be approximated well near its crossover
point by a series in u, where $u=|x-a| Thus, the branch in this case is,
in a sense, artificial, and can be removed by some extra work on the
part of the user.
Baker
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Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
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