Interval analysis and computation

Interval analysis and computation concerns the theory and use in numerical computation of the notion of intervals and arithmetic calculations with them. This is a quite new discipline, though its origin reaches as far as the fifties of the XX century. Currently the use of interval computations steadily spreads out, mostly because it is used as a tool for the so-called validated computations, i.e. computations with quaranteed accuracy taking into account all possible sources of error, from imprecise data to rounding errors during computer calculations.

This pages are devoted mostly to the work of the Qualitative Analysis Group in this area, but they also contain some basic references useful for workers and newcomers to the field.

Basic references and resources:

List of our publications related to this area.
Some general references:
- B. Hayes (2003) A Lucid Interval, American Scientist,
  vol. 91, no. 6, pp. 484-488.
  [A nice and popularly written short introduction to intervals. Mentions my interval diagrams too.]
- R.E. Moore (1966) Interval Analysis. Prentice Hall, Englewood Cliffs, NJ.
  [A classic work, but still worth studying.]
- G. Alefeld, J. Herzberger (1983) Introduction to Interval Computations. Academic Press, New York.
  [A very readable introductory textbook.]
- A. Neumaier (1990) Interval Methods for Systems of Equations. Cambridge University Press, Cambridge.
  [Full of important mathematical results, though hard reading.]
- E. Hansen (1992) Global Optimization Using Interval Analysis. Marcel Dekker, New York.
  [A detailed exposition of the method, lots of benchmark examples.]
- L. Jaulin, M.Kieffer, O.Didrit, É. Walter (2001) Applied Interval Analysis. Springer Verlag, London.
  [Highly recommended for application-oriented readers. An excellent systematization of the approach, clearly written, full of algorithms.]
Selected WWW links:
- The main Interval Computation site at the Department of Computer Science of the University of Texas at El Paso.
- The site of the Reliable Computing journal (formerly Interval Computaions).
- Interval computations software page.
Interval computations mailing lists:
- Main Interval Computation list: <reliable_computing@interval.louisiana.edu>
- Interval Methods in Knowledge Representation list: <interval@cs.utep.edu>
- Validated Numerics (Specific Problems of Interval-Related Software) list: <validated_numerics@tu-harburg.de>
For further information on the lists see the interval lists page at the main Interval Computation site.

Special features:

Information about my recent larger work:
Zenon Kulpa, Diagrammatic Interval Analysis with Applications.
Information about my older larger work:
Zenon Kulpa, From Picture Processing to Interval Diagrams.
A set of LaTEX commands for producing new graphical symbols for basic interval relations [Plain ASCII, 3 KB], see the sample page [Page 185, PDF, 115 KB] from my book above.
A report containing the catalogue of structural types of the basic interval equation a · x = b. This is the next material in the planned series on the diagrammatic approach to interval analysis developed by me.
Good quality scans of two precursory papers on interval analysis by Polish mathematician Mieczyslaw Warmus:
- M. Warmus, Calculus of Approximations. Bull. Acad. Polon. Sci., Cl. III, vol. IV, No. 5 (1956), 253-259.
- M. Warmus, Approximations and Inequalities in the Calculus of Approximations. Classification of Approximate Numbers. Bull. Acad. Polon. Sci., Ser. math., astr. et phys., vol. IX, No. 4, (1961), 241-245.
Materials pertaining to the greatly applauded invited talk of Prof. Jiri Rohn at the SCAN/INTERVAL 2000 International Conference in Karlsruhe on Sept. 18-23, 2000 (the material is posted also on the George Corliss site):
- Lecture slides of the Karlsruhe lecture on "Finite Characterization of Some Linear Problems with Inexact Data" [PDF file, 127KB].
- Appendix with additional remarks and bibliography to the lecture, by J. Rohn [PDF file, 94KB]
- Additional note by J. Rohn posted at the <reliable_computing> mail list and referred to in Paragraph (19) of the Appendix [Plain TEX file, 8KB].

More materials on interesting interval issues to come.

Interval analysis and computation

Basic references and resources:

Special features:

See also: