Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval Standards Working Group]
Dan Zuras Intervals wrote:
>> Cc: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>,
>> stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
>> Content-Transfer-Encoding: 7bit
>> From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
>> Subject: Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE
>> Interval Standards Working Group] Date: Thu, 10 Sep 2009 22:45:10
>> +0100
>> To: Ralph Baker Kearfott <rbk@xxxxxxxxxxxx>
>>
>> On 10 Sep 2009, at 18:36, Ralph Baker Kearfott wrote:
>>> 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,
>>> ...
>>> Of course, there's a very simple operational definition in terms of
>>> the end points :-)
>>
>> And it's equivalent to modal-interval addition of the dual interval,
>> isn't it?
>>
>> John
>
> Yes, just so. There is also an inverse multiply that
> is similarly defined. Nate, you are more qualified to
> discuss this than I am. Anything we need to know? - Dan
The cancellation Baker describes is indeed the "addition of opposite" in
Kaucher/modal intervals, e.g., the interval -[b,a] is the inverse element
(opposite) of [a,b]; and this leads to
[a,b] + (-[b,a]) = [a,b] + [-a,-b] = [a-a,b-b] = [0,0].
Kaucher intervals form a commutative group under addition. If multiplication
by scalar is included, the algebraic structure is a vector space.
S. Markov also shows interesting connections to mid-rad forms in his SCAN
2006 paper, which is on the IEEE 1788 website. Most importantly, he gives a
defintion for multiplication of mid-rad intervals equivalent to the inf-sup
form by E. Kaucher!
Nate Hayes