Optimization Algorithms on Matrix Manifolds

出版者:Princeton Univ Pr

作者:Absil, P. a./ Mahony, Robert/ Sepulchre, Rodolphe

页数:240

出版时间:2007-12

价格:$ 73.45

装帧:HRD

isbn号码:9780691132983

图书标签:流形优化矩阵mainfold_learning数学optimizationMatrixMath

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 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.

用户评价

对流形部分的基础知识介绍很不错，像我这种没学过微分流形的人也能勉强读懂。凸优化部分的理论我没有细看。书中提到的几个算法倒也讲的很仔细，可以当成一本不错的工具书，试不试翻一翻找点灵感啥的。

对流形部分的基础知识介绍很不错，像我这种没学过微分流形的人也能勉强读懂。凸优化部分的理论我没有细看。书中提到的几个算法倒也讲的很仔细，可以当成一本不错的工具书，试不试翻一翻找点灵感啥的。

对流形部分的基础知识介绍很不错，像我这种没学过微分流形的人也能勉强读懂。凸优化部分的理论我没有细看。书中提到的几个算法倒也讲的很仔细，可以当成一本不错的工具书，试不试翻一翻找点灵感啥的。

对流形部分的基础知识介绍很不错，像我这种没学过微分流形的人也能勉强读懂。凸优化部分的理论我没有细看。书中提到的几个算法倒也讲的很仔细，可以当成一本不错的工具书，试不试翻一翻找点灵感啥的。

对流形部分的基础知识介绍很不错，像我这种没学过微分流形的人也能勉强读懂。凸优化部分的理论我没有细看。书中提到的几个算法倒也讲的很仔细，可以当成一本不错的工具书，试不试翻一翻找点灵感啥的。