We use Patricia tries to answer 2-approximate orthogonal range search on a set of n random points and rectangles in k-dimensional space. Given n k-dimensional random points or rectangles and a k-dimensional query rectangle, 2-approximate orthogonal range query counts (or reports) the points in the query rectangle or the rectangles intersecting the query rectangle, allowing errors near the bound...

We present numerical calculations of spherically symmetric radiative transport using a two-moment (P-1) method with a two-dimensional non-linear closure on the Eddington factor. The stationary state solutions contain a critical point. We demonstrate that the two-moment equations with a non-linear closure are well behaved. The solutions are physically acceptable , regular and accurate.

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...

1 Department of Mathematics, Darmstadt University of Technology Schlossgartenstrasse 7, D-64289 Darmstadt, Germany [email protected] 2 Institute of Mathematics ”Simion Stoilow” of the Romanian Academy P.O. Box 1-462, Bucharest, Romania Currently: Department of Mathematics, Darmstadt University of Technology Schlossgartenstrasse 7, D-64289 Darmstadt, Germany leustean@mathemat...

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.

In this technical note, we suggest a new definition for an approximate KKT point. The concept of approximate KKT point can then be used on iterates (points found by an optimization algorithm) to check whether the iterates lead to a KKT point. We will concentrate on the following simple optimization problem (P): Min f(x) subject to gi(x) ≤ 0, i = 1, 2, . . . ,m. (1) We will assume that f and eac...

For problems when decisions are taken prior to observing the realization of underlying random events, probabilistic constraints are an important modelling tool if reliability is a concern. A key concept to numerically dealing with probabilistic constraints is that of pefficient points. By adopting a dual point of view, we develop a solution framework that includes and extends various existing f...

Given non-empty subsets A and B of a metric space, let S : A → B and T : A → B be non-self mappings. Taking into account the fact that, given any element x in A, the distance between x and Sx, and the distance between x and Tx are at least d(A,B), a common best proximity point theorem affirms global minimum of both functions x → d(x, Sx) and x → d(x, Tx) by imposing a common approximate solutio...

Scans acquired by 3D sensors are typically represented in a local coordinate system. When multiple scans, taken from different locations, represent the same scene these must be registered to a common reference frame. We propose a fast and robust registration approach to automatically align two scans by finding two sets of N -points, that are approximately congruent under rigid transformation an...