Report on the Computation of Extremal Polynomials and the Teaching of Hermite Interpolation

Speaker: Dr. Robert Vajda
Date: 11/06/2014
Time: 11:00 - 12:00

Location: RISC Seminar room pond

The author in his PhD thesis and in the talk in the Theroma Seminar last year showed how exact explicit formulas for low degree extremal polynomials can be given with aid of quantifier elimination. In the first part of the talk we report on the progress of that work and compare some viable approaches. In the second part of the talk we report on the work on the teaching of Hermite interpolation. We focus on Neville's recursive idea. Both topics can be interesting to researchers working on automated reasoning as well. The first investigation can be seen as an automated proof of nonexistence of polynomials with certain norms; the correctness of Neville's general recursive algorithm for constructing the Hermite interpolation polynomial can be investigated by the algorithms and tools of automated verification and synthesis. This work is partially supported by the projects OMAA p87öu15, OTKA K83219 and IPA HUSRB1203/221/024.