Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval Standards Working Group]
> Date: Thu, 10 Sep 2009 12:36:49 -0500
> From: Ralph Baker Kearfott <rbk@xxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> CC: stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval
> Standards Working Group]
>
> Dan (and Chenyi, if I may step in),
>
> Cancellation is when you create a sum \sum x_i and need \sum_{i\ne j}
> x_i. You
> then subtract x_i from the sum, but you do it in such a way that there
> isn't overestimation,
> that is, we get, to within roundout error, the same interval as we would
> have if
> we had omitted x_j from the original sum. This is useful, e.g. in
> Gauss--Seidel iteration.
>
> For example, cancellation produces x \cancelminus x = [0,0]
>
> The operation is subtraction, where it is assumed that, in the resulting
> interval,
> every point value in the first operand must be equal to every point
> value in the
> second operand in forming the set of all possible results. (That is, we
> assume dependency.)
>
> Of course, there's a very simple operational definition in terms of the
> end points :-)
>
> How did I do with the explanation, Chenyi?
>
> Baker
>
Got it.
Thank you, Baker.
Yet another success in my ongoing secret plan to
extract a free education from you guys. :-)
Muha ha ha...
Dan