000			02398cam a2200301zu 4500
001			88807826
003			FRCYB88807826
005			20250107210309.0
006			m o d
007			cr un
008			250107s2007 fr | o|||||0|0|||eng d
020			_a9780691132983
035			_aFRCYB88807826
040			_aFR-PaCSA _ben _c _erda
100	1		_aAbsil, P.-A.
245	0	1	_aOptimization Algorithms on Matrix Manifolds _c['Absil, P.-A.', 'Mahony, R.', 'Sepulchre, R.']
264		1	_bPrinceton University Press _c2007
300			_a p.
336			_btxt _2rdacontent
337			_bc _2rdamdedia
338			_bc _2rdacarrier
650		0	_a
700	0		_aAbsil, P.-A.
700	0		_aMahony, R.
700	0		_aSepulchre, R.
856	4	0	_2Cyberlibris _uhttps://international.scholarvox.com/netsen/book/88807826 _qtext/html _a
520			_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.
999			_c60536 _d60536