Given a matrix U , using a deterministic method, we extract a "large" submatrix of Ũ (whose columns are obtained by normalizing those of U ) and estimate its smallest and largest singular value. We apply this result to the study of contact points of the unit ball with its maximal volume ellipsoid. We consider also the paving problem and give a deterministic algorithm to partition a matrix into ...

We construct a probabilistic polynomial time algorithm that computes the mixed discriminant of given n positive definite n × n matrices within a 2O(n) factor. As a corollary, we show that the permanent of an n×n nonnegative matrix and the mixed volume of n ellipsoids inRn can be computed within a 2O(n) factor by probabilistic polynomial time algorithms. Since every convex body can be approximat...

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the timeand space-like geodesics and invariant 1-form on the space of null geodesics. We prove a Poncelet-type theorem for null geodesics on the ellipsoid: if such a geodesic ...

Abstract This paper introduces an algorithm to obtain the probability distribution of the best-fit ellipsoid of an individual random-walk polymer chain from planar projections. This algorithm allows the true three-dimensional behaviour of polymer chains to be inferred from planar experimental measurements such as those obtained by light microscopy. Our algorithm is effective in retrieving the G...

No. title/pages date update file name 1 A note on the elliptic integrals and elliptic functions ellipsoid-may04.tex 3 A note on " Potential flow of a second order fluid over a sphere or an ellipse " ellipse-wang-joseph-apr27.tex 4 A note on flows of a second order fluid around an ellipsoid ellipse-may31a.tex 5 A note on flows of a second order fluid around an ellipsoid of revolution/11pages

Abstract In this paper, we study the minimization of an indefinite quadratic function over intersection balls and linear inequality constraints (QOBL). Using hyperplanes induced by each pair balls, show that optimal solution QOBL can be found solving several extended trust-region subproblems (e-TRS). To solve e-TRS, use alternating direction method multipliers approach a branch bound algorithm....

We present a polynomial-time algorithm for finding one extensive form correlated equilibrium (EFCE) for multiplayer extensive games with perfect recall. This the first such algorithm for an equilibrium notion for games of this generality. The EFCE concept has been defined by von Stengel and Forges [1]. Our algorithm extends the constructive existence proof and polynomial-time algorithm for find...

An Optimal Bounding Ellipsoid (OBE) algorithm with asymptotic convergence properties and a selective update capability is developed in this paper. Interesting geometrical insights into the updating rule are found. This algorithm is shown to be robust with respect to certain model violations. Convergence of the algorithm can be established even when the assumption of bounding ellipsoids breaks d...

We present a numerical algorithm for nonnegative matrix factorization (NMF) problems under noisy separability. An NMF problem under separability can be stated as one of finding all vertices of the convex hull of data points. The research interest of this paper is to find the vectors as close to the vertices as possible in a situation in which noise is added to the data points. Our algorithm is ...