win prizes book price comparison
Search our site
Are You Sleeping by Kathleen Barber Read the opening extract of the brand new Kathleen Barber book before its publication on 27/12/2017

Optimization Algorithms on Matrix Manifolds by P.-A. Absil, R. Mahony, R. Sepulchre
  

Optimization Algorithms on Matrix Manifolds

, ,

Synopsis

Optimization Algorithms on Matrix Manifolds by P.-A. Absil, R. Mahony, R. Sepulchre

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.

Reviews

This book is succinct but essentially self-contained; it includes an appendix with background material as well as an extensive bibliography. The algorithmic techniques developed may be useful anytime a model leads to a mathematical optimization problem where the domain naturally is a manifold, particularly if the manifold is a matrix manifold. The book follows the usual definition-theorem-proof style but it is not intended for traditional course work so there are no exercises. A reader with limited exposure to manifold theory and differential geometry most likely will benefit from consulting standard texts on those subjects first. --Anders Linner, Mathematical Reviews [T]his book is succinct but essentially self-contained; it includes an appendix with background material as well as an extensive bibliography. The algorithmic techniques developed may be useful anytime a model leads to a mathematical optimization problem where the domain naturally is a manifold, particularly if the manifold is a matrix manifold. The book follows the usual definition-theorem-proof style but it is not intended for traditional course work so there are no exercises. A reader with limited exposure to manifold theory and differential geometry most likely will benefit from consulting standard texts on those subjects first. --Anders Linner, American Mathematical Society The book is very well and carefully written. Every chapter starts with a page-long introduction clearly outlining its goals and how they are achieved together with possible relations to other chapters. I find the material very well explained and supported with appropriate examples. It is a pleasure to work with such a book. --Nickolay T. Trendafilov, Foundations of Computational Mathematics


About the Author

P.-A. Absil is associate professor of mathematical engineering at the Universite Catholique de Louvain in Belgium. R. Mahony is reader in engineering at the Australian National University. R. Sepulchre is professor of electrical engineering and computer science at the University of Liege in Belgium.

More books by this author
Author 'Like for Like' recommendations

Loading other formats...

Book Info

Publication date

3rd December 2007

Author

P.-A. Absil, R. Mahony, R. Sepulchre

More books by P.-A. Absil, R. Mahony, R. Sepulchre
Author 'Like for Like'
    recommendations

Publisher

Princeton University Press

Format

Hardback
240 pages

Categories

Applied mathematics
Engineering: general
Computer science

ISBN

9780691132983

The selections are so varied and the reader reviews are so helpful. A fantastic website for those who love books.

Ann Quintilla

I love reading books I wouldn't normally choose before everyone else gets to read them!

Dawn Lynch

My favourite thing about is the 'like for like' page this has really introduced me to some good reads! That and lots of honest reviews.

Sam Lewis

Love books. Love reading. Love reading books. And, here's the trick. Here's a website which caters for people like me.

Ian Harvey-brown

Lovereading tells me about new books before they hit the shelves, lets me find other authors I may like and has great prize draws!

Sheila Dale

Insightful reader reviews and unbiased recommendations. I don't know how I chose books before Lovereading! An essential for all book lovers.

Sarah Harper

Its jam packed with fantastic titles, informative descriptions & fantastic reviews and has a vast array of great features & competitions.

Linda Rollins

It's a lively, independent website with reviews, recommendations and more - with a huge range of books available to buy in all formats.

Alison Layland

Lovereading4kids

Lovereading4schools