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The Resource 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

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

Label
Analytic perturbation theory and its applications
Title
Analytic perturbation theory and its applications
Statement of responsibility
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
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Language
eng
Summary
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
Additional physical form
Also available in print version.
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CaBNVSL
Index
index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Target audience
adult
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
Label
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
Link
http://libproxy.rpi.edu/login?url=http://epubs.siam.org/doi/book/10.1137/1.9781611973143
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Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type MARC source
rdacontent
Contents
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
http://library.link/vocab/cover_art
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unknown
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{'f': 'http://opac.lib.rpi.edu/record=b3556132'}
Extent
1 PDF (xii, 369 pages).
File format
multiple file formats
Form of item
online
Governing access note
Restricted to subscribers or individual electronic text purchasers
Isbn
9781611973143
Media category
electronic
Media MARC source
isbdmedia
Publisher number
OT135
Reformatting quality
access
Specific material designation
remote
System details
  • Mode of access: World Wide Web
  • System requirements: Adobe Acrobat Reader

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