Randomized weakly admissible meshes

Weakly 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.

Geometric weakly admissible meshes, discrete least squares approximations and approximate Fekete points

Using the concept of Geometric Weakly Admissible Meshes (see §2 below) together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete multivariate least squares approximation and Lagrange interpolation.

Low Cardinality Admissible Meshes on Quadrangles, Triangles and Disks

Using classical univariate polynomial inequalities (Ehlich and Zeller, 1964), we show that there exist admissible meshes with O(n2) points for total degree bivariate polynomials of degree n on convex quadrangles, triangles and disks. Higher-dimensional extensions are also briefly discussed. Mathematics subject classification (2010): 41A10, 41A63, 65D10.

Admissible initial growth for diffusion equations with weakly superlinear absorption

Randomized Routing on Meshes with Buses

We give algorithms and lower bounds for the problem of routing k-permutations on d-dimensional MIMD meshes with additional buses. A straightforward argument shows that for all d 1, 2=3 n steps are required for routing permutations (the case k = 1) on a d-dimensional mesh. We prove that routing permutations on d-dimensional meshes requires at least (1 ? 1=d) n steps. For small d better lower bou...