Approximate Fekete Points for Weighted Polynomial Interpolation
نویسنده
چکیده
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 weighted polynomial filters, where the relevant concept is that of weighted norm.
منابع مشابه
On the Calculation of Approximate Fekete Points: the Univariate Case
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.
متن کاملPolynomial approximation and cubature at approximate Fekete and Leja points of the cylinder
The paper deals with polynomial interpolation, least-square approximation and cubature of functions defined on the rectangular cylinder, K = D × [−1, 1], with D the unit disk. The nodes used for these processes are the Approximate Fekete Points (AFP) and the Discrete Leja Points (DLP) extracted from suitable Weakly Admissible Meshes (WAMs) of the cylinder. ¿From the analysis of the growth of th...
متن کاملComputing 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...
متن کاملLocating good points for multivariate polynomial approximation
Locating good points for multivariate polynomial approximation, in particular interpolation, is an open challenging problem, even in standard domains. One set of points that is always good, in theory, is the so-called Fekete points. They are defined to be those points that maximize the (absolute value of the) Vandermonde determinant on the given compact set. However, these are known analyticall...
متن کاملWeakly Admissible Meshes and Discrete Extremal Sets
We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points. These provide new computational tools for polynomial least squares and interpolation on multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs.
متن کامل