Numerical methods -- such as optimization methods, methods for solving systems of equations, etc. -- usually produce approximate solutions. Often, there are no guaranteed bounds on the accuracy of these approximate solutions -- or there are bounds but these bounds are too wide to be practically useful. In such situations, it is desirable to have verified numerical computing, i.e., computing that produces results with verified (provable) accuracy.

When a (final or intermediate) approximate result x of the computation comes with a verified bound D, it means that the actual (unknown) value of the estimated quantity belongs to the interval [x-D,x+D]. In view of this fact, verified numerical computing is also known as interval analysis.

Interval analysis is not only about the bounds. In addition to bounds, we can also have, e.g., partial information about the probabilities of different values from the corresponding intervals or expert information on some of the quantities.

The main purpose of this mini-symposium is to cover the numerical and algorithmic aspects of scientific computing, with a strong emphasis on verification leading to guaranteed properties of computed results as well as on arithmetic, programming, and algorithmic tools that provide and/or enhance this verification.

The intent is to present a state-of-the-art overview on the challenging and dynamic field of verified computing techniques and interval analysis for researchers, experts, and scientists who apply these techniques. We seek contributions that provide competent and concise information on recent hardware and software standards, language support for interval analysis techniques, algorithms with result verification, and applications in various fields.

Paper Submission and Publication The rules of the PPAM conference apply. In particular:

• Papers will be refereed and accepted on the basis of their scientific merit and relevance to the Workshop topics.
• Papers presented at the Workshop will be included into the proceedings and published after the conference by Springer-Verlag in the LNCS series.
• Authors should submit papers (draft version with abstract, PDF file) to Vladik Kreinovich before May 15, 2007. Regular papers are not to exceed 10 pages (LNCS style).
• Final camera-ready versions of accepted papers will be required by October 15, 2007.

Minisymposium Organizers (in alphabetic order):

• Vladik Kreinovich, University of Texas at El Paso, USA
• Bartlomiej Jacek Kubica, Warsaw University of Technology, Poland
• Pawel Sewastjanow, Czestochowa University of Technology, Poland
• Jerzy Wasniewski, Technical University of Denmark, Denmark

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