Analytic perturbation theory and its applications / Konstantin E. Avrachenkov, Inria Sophia Antipolis, Sophia Antipolis, France, Jerzy A. Filar, Flinders University, Adelaide, Australia, Phil G. Howlett, University of South Australia, Adelaide, Australia.
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 th...
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| 100 | 1 | |a Avrachenkov, Konstantin, |e author. |0 http://id.loc.gov/authorities/names/nb2009003927 |1 http://isni.org/isni/0000000055600514. | |
| 245 | 1 | 0 | |a Analytic perturbation theory and its applications / |c Konstantin E. Avrachenkov, Inria Sophia Antipolis, Sophia Antipolis, France, Jerzy A. Filar, Flinders University, Adelaide, Australia, Phil G. Howlett, University of South Australia, Adelaide, Australia. |
| 264 | 1 | |a Philadelphia, Pennsylvania : |b Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), |c 2013. | |
| 300 | |a 1 PDF (xii, 369 pages) | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface -- Introduction and motivation -- Part I. Finite dimensional perturbations -- Inversion of analytically perturbed matrices -- Perturbation of null spaces, eigenvectors, and generalized inverses -- Polynomial perturbation of algebraic nonlinear systems -- Part II. Applications to optimization and Markov process -- Applications to optimization -- Applications to Markov chains -- Applications to Markov decision processes -- Part iii. Infinite dimensional perturbations -- Analytic perturbation of linear operators -- Background on Hilbert spaces and Fourier analysis -- Bibliography -- Index. | |
| 500 | |a Title from title screen, viewed 09/28/2013. | ||
| 520 | 3 | |a 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{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. | |
| 546 | |a English. | ||
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