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 are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior - the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank(TM) and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.

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.


* Chapter 1: Introduction and Motivation* Part I: Finite Dimensional Perturbations* Chapter 2: Inversion of Analytically Perturbed Matrices* Chapter 3: Perturbation of Null Spaces, Eigenvectors, and Generalized Inverses* Chapter 4: Polynomial Perturbation of Algebraic Nonlinear Systems* Part II: Applications to Optimization and Markov Process* Chapter 5: Applications to Optimization* Chapter 6: Applications to Markov Chains* Chapter 7: Applications to Markov Decision Processes* Part III: Infinite Dimensional Perturbations* Chapter 8: Analytic Perturbation of Linear Operators* Chapter 9: Background on Hilbert Spaces and Fourier Analysis* Bibliography* Index

Product Details

  • ISBN13: 9781611973136
  • Format: Hardback
  • Number Of Pages: 384
  • ID: 9781611973136
  • weight: 830
  • ISBN10: 1611973139

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