Re: Moore's new book on interval analysis
Ah, yes, thank you, Arnold, for the short review :-)
As a co-author, I felt it inappropriate to enforce
the "standard notation," since it is not what Ray Moore
uses, and the book uses the same notation Ray has used
since he published his dissertation in the 1960's.
Regarding our motion on notation, I note that the scope
of the motion does not include standardizing notation.
Its scope is only to agree upon what notation we will
be using in the standards document.
Best regards,
Baker
P.S. My main goal for our book was to provide something
to aid beginning students to easily and rapidly
become proficient in the subject.
P.P.S. Although we don't define, in the main narrative,
division by intervals that contain zero, we do
introduce C-Set arithmetic, we use, essentially,
division by zero in an interval Newton method
example (with supplied INTLAB code), we provide
references, we mention that there are different
models depending upon whether or not we include
-\infty and \infty as numbers, and we state that
this is presently controversial. Arnold: Check
the notes at the end of Chapter 8.
P.P.P.S I apologize for the tardy reply. I've been feverishly
making final preparations to send another book to the
publisher.
On 1/30/2009 1:12 PM, Arnold Neumaier wrote:
Ulrich Kulisch wrote:
(in: P1788: Our first formal motion: IR versus *IR)
I think we are talking about mathematics. If mathematics is viewed as
the science of the structures then IR as it is defined in the
StandardNotation is an incomplete entity. With respect to set
inclusion as an order relation it is an ordered set. But the empty
set, for instance, which may be the result of an intersection is
excluded.
Let me mention that the brand new book
R.E. Moore, R B. Kearfott and M.J. Cloud,
Introduction to Interval Analysis,
SIAM, Philadelphia, 2009.
which I got today, treats interval arithmetic on the theoretical level
in the traditional way as the arithmetic of nonempty, closed and bounded
intervals. Division is defined only for denominators not containing zero.
Unfortunately, the book does not conform to the standard notation
paper, although both publications have one of the coauthors in common.
No special symbol is used for the set of all (Moore) intervals.
On the whole, the contents of the book is elementary and fairly
conventional. Notable about the book are
- the final Chapter 11, which references and surveys a large number
of recent application of interval techniques, and
- the use of Intlab throughout the book to illustrate the techniques.
Arnold Neumaier
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(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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