LEADER 04128nam 2200697 a 450 001 9910778220103321 005 20230106004909.0 010 $a1-282-15823-6 010 $a9786612158230 010 $a1-4008-3024-9 024 7 $a10.1515/9781400830244 035 $a(CKB)1000000000788496 035 $a(EBL)457711 035 $a(OCoLC)438732716 035 $a(SSID)ssj0000215768 035 $a(PQKBManifestationID)11202421 035 $a(PQKBTitleCode)TC0000215768 035 $a(PQKBWorkID)10185659 035 $a(PQKB)10385595 035 $a(DE-B1597)446646 035 $a(OCoLC)979757798 035 $a(DE-B1597)9781400830244 035 $a(Au-PeEL)EBL457711 035 $a(CaPaEBR)ebr10312553 035 $a(CaONFJC)MIL215823 035 $a(MiAaPQ)EBC457711 035 $a(PPN)17027084X 035 $a(EXLCZ)991000000000788496 100 $a20090910d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOptimization algorithms on matrix manifolds$b[electronic resource] /$fP.-A. Absil, R. Mahony, R. Sepulchre 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2008 215 $a1 online resource (240 p.) 300 $aDescription based upon print version of record. 311 $a0-691-13298-4 320 $aIncludes bibliographical references (p. [201]-220) and index. 327 $tFrontmatter --$tContents --$tList of Algorithms --$tForeword --$tNotation Conventions --$tChapter One. Introduction --$tChapter Two. Motivation and Applications --$tChapter Three. Matrix Manifolds: First-Order Geometry --$tChapter Four. Line-Search Algorithms On Manifolds --$tChapter Five. Matrix Manifolds: Second-Order Geometry --$tChapter Six. Newton's Method --$tChapter Seven. Trust-Region Methods --$tChapter Eight. A Constellation Of Superlinear Algorithms --$tA. Elements Of Linear Algebra, Topology, And Calculus --$tBibliography --$tIndex 330 $aMany 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. 606 $aMathematical optimization 606 $aMatrices 606 $aAlgorithms 615 0$aMathematical optimization. 615 0$aMatrices. 615 0$aAlgorithms. 676 $a518.1 686 $aSK 915$2rvk 700 $aAbsil$b P.-A$01567725 701 $aMahony$b R$g(Robert),$f1967-$01567726 701 $aSepulchre$b R$g(Rodolphe),$f1967-$028404 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778220103321 996 $aOptimization algorithms on matrix manifolds$93839328 997 $aUNINA