Computing Fekete and Lebesgue points: Simplex, square, disk
نویسندگان
چکیده
منابع مشابه
Computing Fekete and Lebesgue points: Simplex, square, disk
The main purpose of our work is to provide Fekete and Lebesgue points on three basic bidimensional compact sets, the simplex, the square, and the disk, by solving numerically the corresponding large-scale nonlinear optimization problems up to degree n = 18. Our results reach and often improve those previously known [1], [3]. In the case of the simplex, due to their relevance in developing spect...
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In this communication we present a new method to estimate Fekete points on surfaces. Our method works in a general setting, in the sense that we can obtain good estimations of the Fekete points on piecewise regular surfaces. The determination of Fekete points in the unit sphere is considered as a model of a highly non-linear optimization problem with non-linear constraints. In fact, obtaining a...
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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 st...
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We propose a numerical method (implemented in Matlab) for computing algebraic quadrature nodes and weights on compact multivariate domains. It relies on the search of maximum volume submatrices of Vandermonde matrices in suitable polynomial bases, by a greedy algorithm based on QR factorization with column pivoting. Such nodes are approximate Fekete points, and are good also for polynomial inte...
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On the line and its tensor products, Fekete points are known to be the Gauss–Lobatto quadrature points. But unlike high-order quadrature, Fekete points generalize to non-tensor-product domains such as the triangle. Thus Fekete points might serve as an alternative to the Gauss–Lobatto points for certain applications. In this work we present a new algorithm to compute Fekete points and give resul...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2012
ISSN: 0377-0427
DOI: 10.1016/j.cam.2011.12.006