Tuesday, 14 January 2020, 3 p.m. (sharp),

Dr. Daan Huybrechs, KU Leuven,

at the conference room of Dipartimento di Matematica "F. Casorati" - aula Beltrami,in Pavia, will give a lecture titled:

FUNCTION APPROXIMATION WITH REDUNDANCY: STABILITY AND APPLICATIONS

At the end a refreshment will be organized.

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Abstract. It is common to discretize continuous problems in science
and engineering using a basis, a non-redundant set of functions that
is complete in a relevant function space. We show that great
flexibility is gained by allowing redundancy in the discretization.
Using redundancy one can easily deal with domains of complicated
shape, one can introduce known singularities of the solution into the
approximation space, or use other analytical knowledge that does not
match well with a known basis. We supply several examples for partial
differential equations and integral equations. Redundancy does lead to
ill-conditioning of the discretization: we show that with a suitable
strategy, based on least squares approximations, this ill-conditioning
is largely benign and computations can be performed in a stable, and
often even very efficient, manner.