## PIMS/Math Colloquium: Issues in multivariate polynomial interpolation

- Date: 11/06/2009

University of British Columbia

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).