Pacific Institute for the Mathematical Sciences - PIMS

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.

Friday, November 6 at 3pm in MATX 1100

Speaker's 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).