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Re: Potential well and decorations



Ralph Baker Kearfott a écrit :
On 07/04/2011 12:51 PM, Nate Hayes wrote:
Dominique Lohez wrote:
Nate Hayes a écrit :
Dominique Lohez wrote:
.
.
.

If for example we have the interval extension

P(X) = U(X) \union V(X)

with

U(X) = sqrt((|X| \intersect [roundDown(sqrt(a)),+Inf])^2-a)
V(X) = -sqrt(a-(|X| \intersect [0,roundUp(a)]))


If I encountered a function like Dan's, that is,

if (abs(x) > sqrt(a))
    y = sqrt(x^2-a);
else
    y = - sqrt(a-x^2);
end

in a set of computations involving it, rather than
programming it as above, I might, depending on priorities
and relative importance, program it directly in terms of,
say, truncated series, and supply the appropriate
decoration upon return from my "user-supplied" function,
so the arithmetic system would view it as an atomic
operation.  Would that lessen the burden on the
requirements of a decoration scheme?  In any case,
many users may not have the luxury of going down
such a route.

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

IMHO the  point 1 and 2   are better addressed   using set operators

Dominique


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Dr Dominique LOHEZ
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