By P.-A. Absil
Many difficulties within the sciences and engineering will be rephrased as optimization difficulties on matrix seek areas endowed with a so-called manifold constitution. This booklet indicates the best way to make the most the targeted constitution of such difficulties to advance effective numerical algorithms. It locations cautious emphasis on either the numerical formula of the set of rules and its differential geometric abstraction--illustrating how strong algorithms draw both from the insights of differential geometry, optimization, and numerical research. extra theoretical chapters supply readers with the historical past in differential geometry essential to algorithmic improvement. within the different chapters, numerous famous optimization equipment corresponding to steepest descent and conjugate gradients are generalized to summary manifolds. The ebook presents a known improvement of every of those equipment, construction upon the cloth of the geometric chapters. It then courses readers during the calculations that flip those geometrically formulated equipment into concrete numerical algorithms. The cutting-edge algorithms given as examples are aggressive with the simplest current algorithms for a variety of eigenspace difficulties in numerical linear algebra.
Optimization Algorithms on Matrix Manifolds bargains innovations with huge purposes in linear algebra, sign processing, information mining, machine imaginative and prescient, and statistical research. it could possibly function a graduate-level textbook and may be of curiosity to utilized mathematicians, engineers, and laptop scientists.