PIMS/UBC Special Mathematics Colloquium
Carl de Boor
(University of Wisconsin - Madison, USA)
Issues in multivariate polynomial interpolationtional points on
varieties over a discretely valued field
Fri., Nov. 6, 2009, 3:00pm, MATX 1100
Abstract:
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).