(University of Wisconsin - Madison, USA)

While univariate polynomial interpolation has been a basic tool of scientific computing for hundreds of years, multivariate polynomial interpolation is much less understood. Already the question from which polynomial space to choose an interpolant to given data has no obvious answer.

The talk presents, in some detail, one answer to this basic question, namely the ``least interpolant'' of Amos Ron and the speaker which, among other nice properties, is degree-reducing, then seeks some remedy for the resulting discontinuity of the interpolant as a function of the interpolation sites, then addresses the problem of a suitable representation of the interpolation error and the nature of possible limits of interpolants as some of the interpolation sites coalesce.

The last part of the talk is devoted to a more traditional setting, the complementary problem of finding correct interpolation sites for a given polynomial space, chiefly the space of polynomials of degree le k for some k, and ends with a particular recipe for good interpolation sites in the square, the Padua points.

References: http://pages.cs.wisc.edu/~deboor/multiint/

Biosketch:

Carl de Boor is a Professor Emeritus in Mathematics and Computer Science at the University of Wisconsin-Madison. He won the 2003 U.S. National Medal of Science. An expert in numerical analysis, Dr. de Boor is the author of more than 150 papers and four books. He has earned world recognition for his work on spline functions, mathematical expressions that describe free-form curves and surfaces. In particular, Dr. de Boor developed simpler approaches to complex spline calculations, a contribution that revolutionized computer-aided geometric design. His work is now routinely applied in a range of fields that rely on precise geometry, including the use of special effects in films, and in the aircraft and automotive industries. Dr. de Boor grew up in East Germany and came to the United States in 1959. He received a doctorate from the University of Michigan in 1966 and joined the UW-Madison faculty in 1972. Until 2003, Dr. de Boor was the Steenbock Professor of Mathematical Sciences and the P.L. Chebyshev Professor of Mathematics and Computer Sciences. He was awarded the John von Neumann Prize by SIAM in 1996. In 1993 he was elected to the National Academy of Engineering, and in 1997 to the National Academy of Sciences. Dr. de Boor also is a member of the Deutsche Akademie der Naturforscher (1998) and a foreign member of the Polish Academy of Sciences (2000). He holds honorary doctorates from Purdue University (1993) and the Technion in Israel (2002).