04136nam 2200709 a 450 991081780670332120230106004909.01-282-15823-697866121582301-4008-3024-910.1515/9781400830244(CKB)1000000000788496(EBL)457711(OCoLC)438732716(SSID)ssj0000215768(PQKBManifestationID)11202421(PQKBTitleCode)TC0000215768(PQKBWorkID)10185659(PQKB)10385595(DE-B1597)446646(OCoLC)979757798(DE-B1597)9781400830244(Au-PeEL)EBL457711(CaPaEBR)ebr10312553(CaONFJC)MIL215823(PPN)17027084X(FR-PaCSA)88807826(MiAaPQ)EBC457711(EXLCZ)99100000000078849620090910d2008 uy 0engur|n|---|||||txtccrOptimization algorithms on matrix manifolds /P.-A. Absil, R. Mahony, R. SepulchreCourse BookPrinceton Princeton University Press20081 online resource (240 p.)Description based upon print version of record.0-691-13298-4 Includes bibliographical references (p. [201]-220) and index.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 --IndexMany 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 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.Mathematical optimizationMatricesAlgorithmsMathematical optimization.Matrices.Algorithms.518.1SK 915rvkAbsil P.-A1613134Mahony R(Robert),1967-1613135Sepulchre R(Rodolphe),1967-28404MiAaPQMiAaPQMiAaPQBOOK9910817806703321Optimization algorithms on matrix manifolds3942272UNINA