Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

Re: Why saf/saf=con (D4/D4=D2)



Arnold Neumaier wrote:
If one evaluates a function with bare input decorations D4 for every
input argument and gets D4 as the final result, it is known in my
semantics that the function is defined and continuous for all real
inputs. Thus if one performs initially a _single_ bare decoration
calculation and this results in D4, one can safely do subsequent
bare interval computations, and still knows that the results are safe
(i.e., decorated D4) whenever the input is nonempty and bounded.

Such a property may be used to optimize certain computations in
cases where the decorations are handled by software and hence slowly.

With your semantics, one cannot conclude anything from the result D4,
since it is always obtained from D4 inputs, no matter what the
function is.

I'd like to also mention that you present here an interesting and useful use-case. I am still skeptical of D4/D4=D2, but will think some more about this.

Nate Hayes