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Record Nr. |
UNINA9910455230303321 |
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Autore |
Absil P.-A |
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Titolo |
Optimization algorithms on matrix manifolds [[electronic resource] /] / P.-A. Absil, R. Mahony, R. Sepulchre |
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Pubbl/distr/stampa |
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Princeton, : Princeton University Press, 2008 |
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ISBN |
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1-282-15823-6 |
9786612158230 |
1-4008-3024-9 |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (240 p.) |
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Classificazione |
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Altri autori (Persone) |
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MahonyR <1967-> (Robert) |
SepulchreR <1967-> (Rodolphe) |
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Disciplina |
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Soggetti |
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Mathematical optimization |
Matrices |
Algorithms |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. [201]-220) and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- List of Algorithms -- Foreword -- Notation Conventions -- Chapter One. Introduction -- Chapter Two. Motivation and Applications -- Chapter Three. Matrix Manifolds: First-Order Geometry -- Chapter Four. Line-Search Algorithms On Manifolds -- Chapter Five. Matrix Manifolds: Second-Order Geometry -- Chapter Six. Newton's Method -- Chapter Seven. Trust-Region Methods -- Chapter Eight. A Constellation Of Superlinear Algorithms -- A. Elements Of Linear Algebra, Topology, And Calculus -- Bibliography -- Index |
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Sommario/riassunto |
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Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical |
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chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists. |
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