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Re: mid-rad, inf-sup, a caution...

Please see my inserted comment.

Baker

On 5/11/2010 10:00, Chenyi Hu wrote:

Dear All,




Second, there have been some interesting results lately on using interval to model uncertainty. Although I hate to do self-promotion shamelessly, just for your reference, you might want to have a glance on the following (both available online):

"Chapter 4: Interval Matrices in Knowledge Discovery," by Baker and me,

in the  book "Knowledge Processing with Interval and Soft Computing" published by
Springer. In that chapter, we discussed about using mid-rad approach to find
approximate solutions for interval linear systems of equations and SVD/PCA
for interval matrix. The computational approaches may not very suitable with
inf-sup representation.

Actually, there we look at midpoint matrices and width matrices, and look of
ways of finding "approximated" solutions, which approximate the solution
set without regard to whether the "approximated solution" represents an
inner or outer approximation, and we define an "estimation ratio" to measure
how good the approximation is (regardless or whether it is an inner or outer
solution).  Thus, although the results do use intervals, and are novel
and applicable (as evidenced by modeling results in the paper and in
Chenyi's second citation), they
are not concerned with mathematical rigor.  Also, we do not use mid-rad
arithmetic extensively, although we use the mid-rad representation.



"Impacts of Interval Computing on Stock Market Variability Forecasting,"

J. Computational Economics, 2009 33:263-276. Ling T. He and I somewhat compared the mid-rad approach with min-max approach on the stock market forecasting. The mid-rad approach shows clear advantage.


Third, with the above in mind, I advocated mid-rad before in this group. I have to admit that I do not know much about hardware implementation. hence, I do not know how much work would be needed to make mid-rad in the standard. I still remember, when Arnold asked if the standard provide an conversion would meet the needs, I answered yes to this group.

Last, but not the least, experts who knows the complexity of including mid-rad in the standards, please let us know how much more time we need for including mid-rad in the standard. I hope it will not 7 years as Dan mentioned in revising 754 to include decimal.  If I could make a choice, I'd say let us get a standard out as our first priority. Including mid-rad if it does not require too much extra time. Otherwise, leaving it for Version 2.0 might not be a bad idea. Especially, people can use conversion for applications other than finding reliable bounds.

Thanks for your time,

Chenyi

Chenyi Hu

Ph.D., Professor and Chairman
Computer Science Department
University of Central Arkansas
http://www.cs.uca.edu




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R. Baker Kearfott,    rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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