Analytic perturbation theory and its applications
Konstantin E. Avrachenkov, Jerzy A. Filar, Phil G. HowlettAnalytic 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™ 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.
Audience: This text is appropriate for mathematicians and engineers interested in systems and control. It is also suitable for advanced undergraduate, first-year graduate, and advanced, one-semester, graduate classes covering perturbation theory in various mathematical areas.
Contents: 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; Cha