Konstantin E. Avrachenkov, Jerzy A. Filar and Phil G. Howlett
SIAM 2014, 380 PAGES
PRICE (HARDBACK) £60.00 ISBN 978-1-611-97313-6
This book contains nine chapters which are organised into three sections. The first part is concerned with finite dimensional perturbations. The next part deals with applications of these to optimisation and Markov processes, the final part discusses infinite dimensional perturbations.
A description of the chapters follows.
Chapter 1 is a short chapter that introduces the subject and describes various options for using the material in the book.
Chapter 2 is the study of square matrices of finite dimension and their inversion using the Moore-Penrose generalised inverse.
Chapter 3 begins with the study of the analytic perturbation of the null space of square matrices of finite dimension. It continues with rectangular matrices which may or may not be invertible. This chapter uses complex analytic methods.
Chapter 4 begins the study of perturbation of nonlinear algebraic systems by polynomials.
Chapter 5 starts the process of applying the knowledge to optimisation problems.
Chapter 6 applies the knowledge to Markov chains. These are reviewed initially for those unfamiliar with Markov chains, then their behaviour under asymptotic perturbation is analysed.
Chapter 7 describes the application of this knowledge to Markov decision processes.
Chapter 8 introduces the study of perturbation of operators in infinite dimensional spaces, specifically Hilbert and Banach spaces.
Chapter 9 provides some background on Hilbert spaces and Fourier analysis. It is intended as an appendix for students with insufficient background in functional analysis to follow Chapter 8.
The aim of this book is to cover material that is similar to that seen in T. Kato’s book Perturbation Theory for Linear Operators but from a more general viewpoint than spectral analysis. This book is aimed at graduate mathematics students and is at a similar level to Kato’s book.
John Bartlett CMath MIMA
Book review published directly onto IMA website (June 2015)
