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 interpolation. Numerical tests are presented for the interval and the square. 2000 AMS subject classification: Primary 65D05, 65D32; Secondary 65F25.