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Author | : Konstantin E. Avrachenkov |
Publisher | : SIAM |
Total Pages | : 384 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 1611973147 |
Download Analytic Perturbation Theory and Its Applications Book in PDF, ePub and Kindle
Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic 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.
Author | : Konstantin Avrachenkov |
Publisher | : |
Total Pages | : 384 |
Release | : 1999 |
Genre | : Markov processes |
ISBN | : |
Download Analytic Perturbation Theory and Its Applications Book in PDF, ePub and Kindle
Author | : Konstantin E. Avrachenkov |
Publisher | : SIAM |
Total Pages | : 384 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 1611973139 |
Download Analytic Perturbation Theory and Its Applications Book in PDF, ePub and Kindle
Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic 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.
Author | : Tosio Kato |
Publisher | : Springer Science & Business Media |
Total Pages | : 610 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662126788 |
Download Perturbation theory for linear operators Book in PDF, ePub and Kindle
Author | : Takahiro Kawai |
Publisher | : American Mathematical Soc. |
Total Pages | : 148 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 9780821835470 |
Download Algebraic Analysis of Singular Perturbation Theory Book in PDF, ePub and Kindle
The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. This volume is suitable for graduate students and researchers interested in differential equations and special functions.
Author | : Hellmut Baumgärtel |
Publisher | : Birkhauser |
Total Pages | : 0 |
Release | : 1985-04 |
Genre | : Linear operators |
ISBN | : 9780817616649 |
Download Analytic Perturbation Theory for Matrices and Operators Book in PDF, ePub and Kindle
Author | : Aref Jeribi |
Publisher | : Springer Nature |
Total Pages | : 509 |
Release | : 2021-07-28 |
Genre | : Mathematics |
ISBN | : 981162528X |
Download Perturbation Theory for Linear Operators Book in PDF, ePub and Kindle
This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.
Author | : Ferdinand Verhulst |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2006-06-04 |
Genre | : Mathematics |
ISBN | : 0387283137 |
Download Methods and Applications of Singular Perturbations Book in PDF, ePub and Kindle
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Author | : H. Baumgärtel |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 428 |
Release | : 1984-12-31 |
Genre | : Mathematics |
ISBN | : 3112721810 |
Download Analytic Perturbation Theory for Matrices and Operators Book in PDF, ePub and Kindle
No detailed description available for "Analytic Perturbation Theory for Matrices and Operators".
Author | : Petar Kokotovic |
Publisher | : SIAM |
Total Pages | : 386 |
Release | : 1999-01-01 |
Genre | : Mathematics |
ISBN | : 9781611971118 |
Download Singular Perturbation Methods in Control Book in PDF, ePub and Kindle
Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.