apl. Prof. Dr. Knut Petras

Institut für Angewandte Mathematik
Abteilung für Numerische Mathematik
Technische Universität Braunschweig

Pockelsstrasse 14
38106 Braunschweig
Tel. +49 531 391-7538
Fax +49 531 391-8206

e-mail: K.Petras@tu-bs.de

Research interests

• Numerical quadrature
• Numerical cubature
• Information-based complexity
• Approximation theory
• Numerical solution of ordinary differential equations
• Numerical Mathematics with result verification
  ( in particular calculation of integrals and solution of ordinary differential equations )

Additional Information

• In November 2002, I gave a talk on Automatic Differentiation in a Math Education Seminar at Saarbrücken. Here are corresponding informations (in German).
• A database containing a list of recent publications in numerical quadrature and cubature (maintained by Ronald Cools, K.U. Leuven, Belgium)
• A great source of information is Prof. Carl de Boor's Homepage . You can find there delights such as, to give only few examples, loop-free MATLAB , viva_vi ( an introduction to the editor vi ), texts on Approximation Theory , informations on Splines or multivariate polynomial interpolation as well as his special odds and ends
• An essential help for doing mathematics on a computer is the Guide to Available Mathematical Software. A particularly beauti- and useful (but nevertheless not widely known) technique for computing derivatives is Automatic Differentiation. Here is a small collection (written in German) of informations and useful links compiled on the occasion of a talk that I have given at a school.
• If you have to write self-validating numerical software, an essential tool is a package providing interval arithmetic. One possible choice is one of the XSC-languages. German and english descriptions of PASCAL-XSC are available. There is already existing software
• Neverending sources of interesting mathematical ideas in the area of Information-based complexity are, e.g., Erich Novak, Klaus Ritter, Greg Wasilkowski or Henryk Wozniakowski.
• Here is another sample of a Homepage of an outstanding mathematician
• Mathematical Departments in German Universities
• Mathematical Departments in the USA
• There are further useful links at the bottom of Kai Diethelm's Homepage or at the link-page of the Mathematical Institute of the University of Munich
• This page was produced with the help of several HTML-documentations. Useful hints are welcome!

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  Knut Petras