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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Recent Results on Rational Approximation and Inter
polation with Completely and Multiply Monotone Rad
ial Basis Functions - Martin Buhmann (Justus-Lie
big-Universität Gießen)
DTSTART;TZID=Europe/London:20190220T110000
DTEND;TZID=Europe/London:20190220T113500
UID:TALK120124AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/120124
DESCRIPTION:We will report on new results about approximations
to continuous functions of multiple variables.&nb
sp\;We shall use either approximation with interpo
lation or approximation by rational functions. For
these kinds of approximations\, radial basis func
tions are particularly attractive\, as they provid
e regular\, positive definite or conditionally pos
itive definite approximations\, independent of the
spatial dimension and independent the distributio
n of the data points we wish to work with. These i
nterpolants have very many applications for exampl
e in solving nonlinear partial differential equati
ons by collocation. \;In this talk\, we classi
fy radial basis and other functions that are usefu
l for such scattered data interpolation or for rat
ional approximations from vector spaces spanned by
translates of those basis functions (kernels)\; f
or this we study in particular multiply and/or com
pletely monotone functions. We collect special pro
perties of such monotone functions\, generalise th
em and find larger classes than the well known mon
otone functions for multivariate interpolation. Fu
rthermore\, we discuss efficient ways to compute r
ational approximations using the same type of kern
els.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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