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Books Year : 2013

Analytic Perturbation Theory and Its Applications


We live in an era in which mathematical models--or systems--are used to describe complex phenomena (climate change dynamics, stock markets, the Internet, logistics, etc.). These systems typically depend on one or more parameters that are assigned nominal values based on current understanding of the phenomena. Because these values are usually estimates, it is important to know how even small deviations from them affect the behavior of the system. Single-parameter deviations pose significant technical challenges, but they constitute a natural starting point, especially since much progress has been made in analyzing the asymptotic behavior of these deviations in many special settings in the sciences, engineering, and economics. This book considers systems that can be disturbed to varying degrees by changing the value of a single perturbation parameter. The difference between the actual and nominal values of this key parameter, the perturbation, is small but unknown in most applications, so it is important to understand the behavior of the solutions as the perturbation tends to zero. Many interesting applications contain an apparent discontinuity in the limiting behavior that complicates the analysis. These are the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes * comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses, generalized inverses, and polynomial systems, topics not covered in other books; * 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.
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Dates and versions

hal-00926397 , version 1 (09-01-2014)



Konstantin Avrachenkov, Jerzy Filar, Phil Howlett. Analytic Perturbation Theory and Its Applications. SIAM, pp.372, 2013, 978-1611973136. ⟨10.1137/1.9781611973143⟩. ⟨hal-00926397⟩


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