Optimization Algorithms on Matrix Manifolds

Optimization Algorithms on Matrix Manifolds
Автор
 
Год
 
Страниц
 
240
ISBN
 
0691132984
Издатель
 
Princeton University Press

Содержание:

Книга 1, CompTIA Security+: Study Guide (+ CD-ROM), Книга 2, Security Administrator Street Smarts, Книга 3, Security+: Fast Pass (+ CD-ROM)

Описание:

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...

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