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# Xstar\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {X}}_{star}$$\end{document} for a design with 3 support points, where X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {X}}$$\end{document} is a discretized square [-1,1]2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[-1,1]^2$$\end{document}. The support points are denoted by black circles, and the gray dots form the star sets

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We propose an algorithm for computing efficient approximate experimental designs that can be applied in the case of very large grid-like design spaces. Such a design space typically corresponds to the set of all combinations of multiple genuinely discrete factors or densely discretized continuous factors. The proposed algorithm alternates between t...

## Citations

... In contrast, if X is an infinite set (or a continuum), a good finite representer, sayX, of X must be constructed first. There are several approaches to attack such a problem, treatingX as a variable or a fixed parameter of the problem, which is chosen accordingly to certain heuristics as space filling techniques, grid exploration (see e.g., [8]), or minimal spanning tree. Recently, it has been shown that the use of polynomial admissible meshes gives precise quantitative estimates of the approximation intruduced in the discretization of the problem , i.e., when passing from X toX, see [5]. ...

Optimal experimental designs are probability measures with finite support enjoying an optimality property for the computation of least squares estimators. We present an algorithm for computing optimal designs on finite sets based on the long-time asymptotics of the gradient flow of the log-determinant of the so called information matrix. We prove the convergence of the proposed algorithm, and provide a sharp estimate on the rate its convergence. Numerical experiments are performed on few test cases using the new matlab package OptimalDesignComputation.