Excerpts from: Interval Computations: Introduction, Uses, and Resources

Email: rbk@louisiana.edu
Office telephone: (318) 482-5270
Fax: (318) 482-5346

The following are excerpts from the article Interval Computations: Introduction, Uses, and Resources that appeared in the Euromath Bulletin 2 (1). These excerpts point to resources that are available on the internet. Please send any error reports or suggested enhancements to me. The sections are

• 5.1.1 General Internet Pages
• 5.1.2 Bibliographies
• 5.1.3 Software
• 5.1.4 Mailing List (Discussion Group)
• 5.2 Journals
• 5.3 Books
• 5.4. Conferences
• 6. Researchers and Research Centers
• 7. Summary

  ---

  5. Brief Guide to Resources

  
  

  5.1 Internet Resources

  5.1.1 General Internet Pages

  A primary entry point to items concerning interval computations is the page:
  http://cs.utep.edu/interval-comp/main.html
  This page contains pointers to much of the information in this article: Namely, it provides an elementary description of interval computations, programming languages for interval computations, home pages of interval computations researchers, information about the journal Reliable Computing, bibliographies, etc. This page is maintained by Vladik Kreinovich and Misha Koshelev at the University of Texas at El Paso. Arnold Neumaier maintains a home page for global optimization (including interval computations) at:
  http://solon.cma.univie.ac.at/~neum/glopt.html
  

  ---

  5.1.2 Bibliographies

  • Bohlender has a bibliography, in LaTeX, that contains approximately 1000 entries in {\BibTeX} format, at
    http://ma70.rz.uni-karlsruhe.de/~ae15/litlist.html
    Although not comprehensive, this list contains references related to the work at the University of Karlsruhe, as well as other interesting references.
  • Nelson Beebe and Jon Rokne maintain a BibTeX bibliography at:
    ftp://ftp.math.utah.edu/pub/tex/bib/intarith.bib
    (the TeX DVI file):
    ftp://ftp.math.utah.edu/pub/tex/bib/intarith.dvi
    This bibliography is based upon but extends a two-thousand entry bibliography previously published in the Freiburger Intervallberichte.
  • The Freiburger Intervallberichte bibliography itself is available at:
    href=http://solon.cma.univie.ac.at/~neum/intlib
    

  ---

  5.1.3 Software

  Software, as follows, is available free of charge over the Internet.
  • PROFIL/BIAS is a C/C++ package, developed by Jansson and Knüppel at Hamburg, that implements an interval data type. It also has substantial support for linear algebra operations, and is notably fast.
  • INTLIB is a library of FORTRAN~77 routines for interval arithmetic operations and interval values of standard functions.
  • INTLIB_90 is a Fortran~90 module that defines an interval data type, with support for various standard functions. A corresponding writeup (accepted for publication in the ACM Transactions on Mathematical Software) is INTERVAL_ARITHMETIC: An Interval Data Type.
  • C-XSC is one of the well-known "XSC" languages developed under the direction of Prof. Dr. Kulisch at Universität Karlsruhe. The version of the entire package is available free of charge for the Borland C++ compiler version 4.x.
  Additional software is available through other distribution channels or for a price. For further information, consult:
  http://cs.utep.edu/interval-comp/main.html

  ---

  5.1.4 Mailing List (Discussion Group)

  There is an interval mailing list. This amiable discussion group is managed automatically by the Majordomo software. The list presently consists of roughly 450 subscribers across the world. Items such as conference announcements, problems and solutions, announcements of book publications, and similar information typically are posted here. To send a message to the entire list, send the message to:
  reliable_computing@interval.louisiana.edu
  To subscribe to the mailing list, send a message to:
  majordomo@interval.louisiana.edu
  The body of the message should consist of the line:
  
  subscribe reliable_computing
  Persons may just as easily remove themselves from the list or obtain the email addresses on the list. Details are sent upon subscription to the list.
  

  ---

  5.2 Journals

  The journal Interval Computations started as a joint Soviet-Western enterprise in 1991, and continues as the journal Reliable Computing.
  Besides that, Computing commonly publishes material related to interval computations, as well as the journal Journal of Global Optimization. Traditional numerical analysis journals, such as BIT, the SIAM Journal on Numerical Analysis, the SIAM Journal on Scientific and Statistical Computing, the Mathematics of Computation, and the ACM Transactions on Mathematical Software contain articles on interval computations.
  

  ---

  5.3 Books

  (Work is still being done on this part. If you have URL's for your book or conference proceedings, please send them to me.
  

  ---

  5.4. Conferences

  Numerous conferences on the subject have been held. Perhaps the most well-known of these are the "SCAN" (Society for Computer Arithmetic and Numerics) meetings, generally held biennially in the Fall in Europe, and sponsored by IMACS and GAMM. (The last two have been SCAN'93 in Vienna and SCAN'95 in Wuppertal.) R. E. Moore held a meeting in Columbus, Ohio in 1987. INTERVAL'92 was held in St. Petersburg, Russia, INTERVAL'94 was held in Moscow, and INTERVAL'96 will be held in Würzburg in September, 1996. S. Markov organized conferences on mathematical modeling and scientific computing, heavily featuring interval computations, in Albena, Bulgaria in 1991 and in Sozopol, Bulgaria in 1993. The conference on Numerical Analysis with Automatic Result Verification was held in Lafayette, Louisiana in 1993. A workshop on interval arithmetic will take place in Recife, Brazil in August, 1996. Click here for some details of upcoming conferences.
  

  ---

  6. Researchers and Research Centers

  Click here for a list of home pages of various researchers. Researchers not mentioned there should contact Prof. Vladik Kreinovich, who maintains the Web page on researchers.
  

  ---

  7. Summary

  This paper has briefly introduced the subject of interval computations, and has guided the reader to electronic and printed material for further study and research.