Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 1-12.


Weakly Admissible Meshes and Discrete Extremal Sets

Len Bos 1, Stefano De Marchi 2*, Alvise Sommariva 2, Marco Vianello 2

1 Department of Computer Science, University of Verona, Strada Le Grazie 15 - 37134 Verona, Italy.
2 Department of Pure and Applied Mathematics, University of Padua, Via Trieste 63 - 35121 Padua, Italy.

Received 8 March 2010; Accepted (in revised version) 8 June 2010
Abstract

We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points. These provide new computational tools for polynomial least squares and interpolation on multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs.

AMS subject classifications: 65D05, 65D32
Key words: Weakly admissible meshes, Approximate Fekete points, Discrete Leja points.
*Corresponding author.
Email: leonardpeter.bos@univr.it (L. Bos), demarchi@math.unipd.it (S. De Marchi), alvise@math.unipd.it (A. Sommariva), marcov@math.unipd.it (M. Vianello)
 

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