Computing approximate Fekete points by QR factorizations of Vandermonde matrices
نویسندگان
چکیده
منابع مشابه
Computing approximate Fekete points by QR factorizations of Vandermonde matrices
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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We give an algorithm for computing approximate PSD factorizations of nonnegative matrices. The running time of the algorithm is polynomial in the dimensions of the input matrix, but exponential in the PSD rank and the approximation error. The main ingredient is an exact factorization algorithm when the rows and columns of the factors are constrained to lie in a general polyhedron. This strictly...
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We compute approximate Fekete points for weighted polynomial interpolation by a recent algorithm based on QR factorizations of Vandermonde matrices. We consider in particular the case of univariate and bivariate functions with prescribed poles or other singularities, which are absorbed in the basis by a weight function. Moreover, we apply the method to the construction of real and complex weigh...
متن کاملComputing Multivariate Fekete and Leja Points by Numerical Linear Algebra
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 discuss some theoretical aspects of the univariate case of the method recently introduced by Sommariva and Vianello [12] for the calculation of approximate Fekete points for polynomial interpolation.
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2009
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2008.11.011