Analytic Perturbation Theory and its Applications

Analytic Perturbation Theory and its Applications

By: Phil G. Howlett (author), Konstantin E. Avrachenkov (author), Jerzy A. Filar (author)Hardback

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Mathematical models, vital to our understanding of complex phenomena, typically depend on parameters that are assigned nominal values based on current understanding of the system in question. As these values are usually estimates, it is important to know how even small perturbations of them affect the behavior of the model. This book considers systems that can be disturbed to varying degrees by changing the value of a single perturbation parameter. It includes comprehensive treatment of analytic perturbations of matrices and linear operators, particularly the singular perturbation of inverses, generalized inverses, and polynomial systems. It also presents original applications to topics that include Markov decision processes, optimisation, search engine rankings, and the Hamiltonian cycle problem. This text is appropriate for pure and applied mathematicians and engineers interested in systems and control. Every chapter includes a problem section, making it suitable for a graduate course in perturbation theory.

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About Author

Konstantin E. Avrachenkov is Director of Research at INRIA Sophia Antipolis, France. He is an associate editor of the International Journal of Performance Evaluation and has published more than 40 journal and 50 refereed conference articles. His main research interests are Markov processes, singular perturbation theory, queuing theory, mathematical programming, game theory, and performance evaluation of communication networks. Jerzy A. Filar is Director of Flinders Mathematical Sciences Laboratory at Flinders University, Australia. He is a co-author of Competitive Markov Decision Processes (1996) and has authored or co-authored approximately 100 refereed research papers. He is a Fellow of the Australian Mathematical Society. His research interests span both theoretical and applied topics in operations research, optimisation, game theory, applied probability, and environmental modelling. Phil G. Howlett is Emeritus Professor of Industrial and Applied Mathematics, University of South Australia. He is a member and former Leader of the Scheduling and Control Group (SCG) in the Centre for Industrial and Applied Mathematics (CIAM) and a member of the Barbara Hardy Institute. He was Director of CIAM, 1998-2004; Director of the Australian Mathematics-in-Industry Study Group, 2000-2003; and Chair of ANZIAM (Australia and New Zealand Industrial and Applied Mathematics), 2008-2009. He has worked on the development of optimal driving strategies for trains and solar-powered racing cars and on railway operations efficiency as well as other areas of applied mathematics, including recent work on management of water supply systems, rainfall modelling, and singular perturbations of linear operators.


Preface; 1. Introduction and motivation; Part I. Finite Dimensional Perturbations: 2. Inversion of analytically perturbed matrices; 3. Perturbation of null spaces, eigenvectors, and generalized inverses; 4. Polynomial perturbation of algebraic nonlinear systems; Part II. Applications to Optimization and Markov Process: 5. Applications to optimization; 6. Applications to Markov chains; 7. Applications to Markov decision processes; Part III. Infinite Dimensional Perturbations: 8. Analytic perturbation of linear operators; 9. Background on Hilbert spaces and Fourier analysis; Bibliography; Index.

Product Details

  • publication date: 16/01/2014
  • ISBN13: 9781611973136
  • Format: Hardback
  • Number Of Pages: 380
  • ID: 9781611973136
  • weight: 830
  • ISBN10: 1611973139

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