RE: a book of potential interest to interval researchers All, If the criterion to "belonging" to interval arithmetic is whether or not interval researchers work on it, then the result is a resounding "yes."  Ask Jiri Rohn, G{\\"o}tz Alefeld, or Sergey Shary, (among others) for example.   I view "interval arithmetic" as striving to compute sharp bounds on ranges, in a way that takes account of machine arithmetic.  This may, at times, go beyond use of the pre-programmed four basic "arithmetic" operations;  I think the goal should take us wherever is appropriate, and we should not get too stuck on what the subject is called, except, of course, if it would otherwise lead to technical confusion, or for promotional purposes :-) Best regards, Baker At 10:31 PM 2/16/2005 +0100, Andrzej Pownuk wrote: >Dear interval researchers, > >I have general question related to the problem, >what is interval arithmetic and what is not interval arithmetic. > >As far as I know interval arithmetic >is based on the functions with interval parameters in the following form: > >z=f(x)         e.g. [-1, 1] = sin([-10, 10]) > >or > >z=f(x,y) >e.g. >[2,5]=+([1,2],[1,3]) or [2,5]=[1,2]+[1,3] > >[1,6]=*([1,2],[1,3]) or [1,6]=[1,2]*[1,3] > >i.e. f=+,-,*,/. > >However, according to my knowledge >in most of the books which are related to interval arithmetic >there are information about systems of linear interval equations. >In this case relation between input and output interval parameters is much >more complicated. > >Y=hull{{x: Ax=B, A belong to [A], B belong to [B]} > >We have also united solution set, tolerable solution set, >controllable solution set etc. > >My question is. > >**************************************************************************** >Does theory of systems of linear interval equations belong >to interval arithmetic or not? >**************************************************************************** > >If more complicated relations on intervals >(e.g. system of linear interval equations) also belong >to interval arithmetic >then maybe all functions on intervals are some extensions >of interval arithmetic. > >I suspect that the authors of the presented book >(i.e. Uncertain Input Data Problems and the Worst Scenario Method) >work on some functions with intervals or set valued parameters >(I am not sure, I do not know that book). >Then from that point of view >they are working on some extension of interval arithmetic. > >Regards, > >Andrzej Pownuk > >--------------------------------------------- >Ph.D., research associate at: >Chair of Theoretical Mechanics >Faculty of Civil Engineering >Silesian University of Technology >ul. Krzywoustego 7 >44-100Â  Gliwice, Poland > >Tel/fax: 0048 32 2371542 >Mobile:Â  0048 606 550147 > >URL:Â Â Â  http://zeus.polsl.gliwice.pl/~pownuk >E-mail: pownuk@zeus.polsl.gliwice.pl >--------------------------------------------- > >I agree. > >I have ordered it from Amazon.Â  Perhaps the authors don't know >about intervals.Â  Many people still do not. > >The encouraging thing is that even point people are starting >to realize the importance of input uncertainty.Â  This can only >be good for us. :) > >Cheers, > >Bill > >P.S. If nothing else, this is a source of good examples for >you to use in your talk. :) > > >Ray Moore wrote: > >> It seems odd to me that there is no mention of interval computation in >> the book. >> >> Ray Moore >> >> ----- Original Message ----- From: "Vladik Kreinovich" > >> To:  >> Cc:  >> Sent: Wednesday, February 16, 2005 12:27 AM >> Subject: a book of potential interest to interval researchers >> >> >>> Forwarding, from NA Digest >>> ****************************************** >>> From: Jan Chleboun  >>> Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET) >>> Subject: New Book on Uncertain Input Data >>> >>> Uncertain Input Data Problems and the Worst Scenario Method >>> by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska; >>> North-Holland Series in Applied Mathematics and Mechanics, Volume 46, >>> Elsevier, Amsterdam, December 2004. >>> Hardback, xxvi+458 pages, ISBN: 0-444-51435-X >>> >>> This book deals with the impact of uncertainty in input data on the >>> outputs of mathematical models. Uncertain inputs as scalars, tensors, >>> functions, or domain boundaries are considered. In practical terms, >>> material parameters or constitutive laws, for instance, are uncertain, >>> and >>> quantities as local temperature, local mechanical stress, or local >>> displacement are monitored. The goal of the worst scenario method is to >>> extremize the quantity over the set of uncertain input data. >>> >>> A general mathematical scheme of the worst scenario method, including >>> approximation by finite element methods, is presented, and then >>> applied to >>> various state problems modeled by differential equations or variational >>> inequalities: nonlinear heat flow, Timoshenko beam vibration and >>> buckling, >>> plate buckling, contact problems in elasticity and thermoelasticity with >>> and without friction, and various models of plastic deformation, to list >>> some of the topics. Dozens of examples, figures, and tables are included. >>> >>> More details can be found at >>> http://books.elsevier.com/elsevier/?isbn=044451435X >>> >>> Jan Chleboun >>> Mathematical Institute >>> Academy of Sciences >>> Zitna 25Â  ( TeX: \\v{Z}itn\\'a ) >>> 115 67 Prague 1 >>> Czech Republic >>> e-mail: chleb@math.cas.cz >>> >>> >> > > > > --------------------------------------------------------------- R. Baker Kearfott,    rbk@louisiana.edu   (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 ---------------------------------------------------------------