期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 57, 期 8, 页码 1324-1336出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2008.11.011
关键词
Approximate Fekete points; Vandermonde matrices; Maximum volume submatrices; Greedy algorithm; QR factorization with column pivoting; Algebraic quadrature; Polynomial interpolation; Lebesgue constant; Admissible mesh
资金
- ex-60% funds of the University of Padova
- INdAM GNCS
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. (c) 2009 Elsevier Ltd. All rights reserved.
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