Computing approximate Fekete points by QR factorizations of Vandermonde matrices

We propose a numerical method (implemented in Matlab) for computing approximate Fekete points on compact multivariate domains. It relies on the search of maximum volume submatrices of Vandermonde matrices computed on suitable discretization meshes, and uses a simple greedy algorithm based on QR fact...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 57; no. 8; pp. 1324 - 1336
Main Authors Sommariva, Alvise, Vianello, Marco
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2009
Subjects
Admissible mesh
Algebraic quadrature
Approximate Fekete points
Greedy algorithm
Lebesgue constant
Maximum volume submatrices
Polynomial interpolation
QR factorization with column pivoting
Vandermonde matrices
Lebesgue constant
Admissible mesh
QR factorization with column pivoting
Polynomial interpolation
Maximum volume submatrices
Greedy algorithm
Approximate Fekete points
Vandermonde matrices
Algebraic quadrature
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Summary:We propose a numerical method (implemented in Matlab) for computing approximate Fekete points on compact multivariate domains. It relies on the search of maximum volume submatrices of Vandermonde matrices computed on suitable discretization meshes, and uses a simple greedy algorithm based on QR factorization with column pivoting. The method gives also automatically an algebraic cubature formula, provided that the moments of the underlying polynomial basis are known. Numerical tests are presented for the interval and the square, which show that approximate Fekete points are well suited for polynomial interpolation and cubature.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2008.11.011