This book, the first on these topics, addresses the problem of finding an ellipsoid to represent a large set of points in high-dimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. Due to the high dimensionality of these problems, first-order methods that require minimal computational work at each iteration ...
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This book, the first on these topics, addresses the problem of finding an ellipsoid to represent a large set of points in high-dimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. Due to the high dimensionality of these problems, first-order methods that require minimal computational work at each iteration are attractive. While algorithms of this kind have been discovered and rediscovered over the past fifty years, their computational complexities and convergence rates have only recently been investigated. The optimization problems in the book have the entries of a symmetric matrix as their variables, so the author's treatment also gives an introduction to recent work in matrix optimization.* Provides historical perspective on the problems studied by optimizers, statisticians, and geometric functional analysts.* Demonstrates the huge computational savings possible by exploiting simple updates for the determinant and the inverse after a rank-one update.* Highlights the difficulties in algorithms when related problems are studied that do not allow simple updates at each iteration.* Gives rigorous analyses of the proposed algorithms, MATLAB codes, and computational results.
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Add this copy of Minimum-Volume Ellipsoids: Theory and Algorithms to cart. $84.00, Sold by Zubal Books rated 4.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 2016 by SIAM-Society for Industrial and Applied Mathematics.
Edition:
2016, Society for Industrial & Applied Mathematics,U.S.
Publisher:
Society for Industrial & Applied Mathematics,U.S.
Published:
2016
Alibris ID:
18026566624
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163 pp., paperback, NEW! ! ! . -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
