Analytic Perturbation Theory and Its Applications
Analytic Perturbation Theory and Its Applications
Jerzy A. Filar, Flinders University of South Australia
Phil G. Howlett, University of South Australia
$94.99
USDMathematical 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.
- A comprehensive treatment of analytic perturbations of matrices and linear operators
- Presents applications in Markov decision processes, optimization, Google PageRank, the Hamiltonian cycle problem, and input retrieval in linear control systems
- Every chapter contains a problem section to aid readers and course instructors
Product details
January 2014Hardback
9781611973136
380 pages
262 × 183 × 20 mm
0.83kg
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Table of Contents
- 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.
