Thursday,
March 3, 4:30 p.m.
Lloyd N. Trefethen
University of Oxford
Robust Rational Interpolation
Abstract
Approximating functions or data by polynomials is an everyday
tool, starting with Taylor series. Approximating by rational
functions can be much more powerful, but also much more
troublesome. In different contexts rational approximations may
fail to exist, fail to be unique, or depend discontinuously
on the data. Some approximations show forests of seemingly
meaningless pole-zero pairs or "Froissart doublets", and when
these artifacts should not be there in theory, they often
appear in practice because of rounding errors on the computer.
Yet for some applications, like extrapolation of sequences and
series, rational approximations are indispensable.
In joint work with Pedro Gonnet and Ricardo Pachon we have
developed a method to get around most of these problems in
rational interpolation and least-squares fitting, based on
the singular value decomposition. The talk will show many
examples of the performance of our "ratdisk" code, including
an application to radial basis function interpolation.
