Approximate Fekete points for weighted polynomial interpolation
In the present paper, which is mainly of computational and experimental character, the authors focus on approximating Fekete points for weighted polynomial interpolation on compact sets. A recent algorithm [cf. \textit{A. Sommariva} and \textit{M. Vianello}, Comput. Math. Appl. 57, No. 8, 1324--1336 (2009; Zbl 1186.65028)] based on QR factorization with column pivoting [\textit{P. A. Businger} and \textit{G. H. Golub}, Numer. Math. 7, 269--276 (1965; Zbl 0142.11503)] of Vandermonde matrices is employed. In particular cases of univariate and bivariate functions with prescribed poles or other singularities, which are absorbed in the basis by a weight function, are considered. The method is also applied to the construction of real and complex weighted polynomial filters, where the relevant concept is that of weighted norm.
scientific article; zbMATH DE number 5692982