Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra

Authors:
L. Bos;S. De Marchi;A. Sommariva;M. Vianello
Affiliations:
leonardpeter.bos@univr.it;demarchi@math.unipd.it and alvise@math.unipd.it and marcovi@math.unipd.it;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

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Abstract

We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. The second computes discrete Leja points by LU factorization with row pivoting. Moreover, we study the asymptotic distribution of such points when they are extracted from weakly admissible meshes.