Analytic Perturbation Theory and Its Applications

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.