Authors:Luc Pronzato, Henry P. Wynn, Anatoly A Zhigljavsky,
Publisher: Chapman and Hall/CRC
Keywords: dynamical, search, crc, statistics, hall, interdisciplinary, chapman, applications, systems, optimization, amp
Number of Pages: 240
Published: 1999-08-27
List price: $134.95
ISBN-10: 0849303362
ISBN-13: 9780849303364

Certain algorithms that are known to converge can be renormalized or "blown up" at each iteration so that their local behavior can be seen. This creates dynamical systems that we can study with modern tools, such as ergodic theory, chaos, special attractors, and Lyapounov exponents. Furthermore, we can translate the rates of convergence into less studied exponents known as Renyi entropies. This all feeds back to suggest new algorithms with faster rates of convergence. For example, in line-search, we can improve upon the Golden Section algorithm with new classes of algorithms that have their ow