Perturbations

Author : James A. Murdock
Publisher : SIAM
ISBN 13 : 9781611971095
Total Pages : 358 pages
Book Rating : 4.98/5 ( download)

DOWNLOAD NOW!

Download or read book Perturbations written by James A. Murdock and published by SIAM. This book was released on 1999-01-01 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.

Author : Tamir Hazan
Publisher : MIT Press
ISBN 13 : 0262549948
Total Pages : 413 pages
Book Rating : 4.43/5 ( download)

DOWNLOAD NOW!

Download or read book Perturbations, Optimization, and Statistics written by Tamir Hazan and published by MIT Press. This book was released on 2023-12-05 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees. In nearly all machine learning, decisions must be made given current knowledge. Surprisingly, making what is believed to be the best decision is not always the best strategy, even when learning in a supervised learning setting. An emerging body of work on learning under different rules applies perturbations to decision and learning procedures. These methods provide simple and highly efficient learning rules with improved theoretical guarantees. This book describes perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees, offering readers a state-of-the-art overview. Chapters address recent modeling ideas that have arisen within the perturbations framework, including Perturb & MAP, herding, and the use of neural networks to map generic noise to distribution over highly structured data. They describe new learning procedures for perturbation models, including an improved EM algorithm and a learning algorithm that aims to match moments of model samples to moments of data. They discuss understanding the relation of perturbation models to their traditional counterparts, with one chapter showing that the perturbations viewpoint can lead to new algorithms in the traditional setting. And they consider perturbation-based regularization in neural networks, offering a more complete understanding of dropout and studying perturbations in the context of deep neural networks.

Author : L.S. Frank
Publisher : Elsevier
ISBN 13 : 9780080875446
Total Pages : 554 pages
Book Rating : 4.40/5 ( download)

DOWNLOAD NOW!

Download or read book Singular Perturbations I written by L.S. Frank and published by Elsevier. This book was released on 1990-08-16 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singular perturbations, one of the central topics in asymptotic analysis, also play a special role in describing physical phenomena such as the propagation of waves in media in the presence of small energy dissipations or dispersions, the appearance of boundary or interior layers in fluid and gas dynamics, as well as in elasticity theory, semi-classical asymptotic approximations in quantum mechanics etc. Elliptic and coercive singular perturbations are of special interest for the asymptotic solution of problems which are characterized by boundary layer phenomena, e.g. the theory of thin buckling plates, elastic rods and beams. This first volume deals with linear singular perturbations (on smooth manifolds without boundary) considered as equicontinuous linear mappings between corresponding families of Sobolev-Slobodetski's type spaces of vectorial order.

Author : Helene Lefebvre-Brion
Publisher : Elsevier
ISBN 13 : 0323150764
Total Pages : 429 pages
Book Rating : 4.67/5 ( download)

DOWNLOAD NOW!

Download or read book Perturbations in the Spectra of Diatomic molecules written by Helene Lefebvre-Brion and published by Elsevier. This book was released on 2012-12-02 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbations in the Spectra of Diatomic Molecules examines in sufficient detail the spectrum of every diatomic molecule. This book is divided into seven chapters. Chapter 1 describes the perturbations and simple procedures for evaluating matrix elements of angular momentum. The terms in the molecular Hamiltonian that are responsible for perturbations are elaborated in Chapter 2, while the process of reducing spectra to molecular constants and the difficulty of relating empirical parameters to terms in the exact molecular Hamiltonian are described in Chapter 3. Chapter 4 discusses the magnitudes and physical interpretations of matrix elements. The transition intensities, especially quantum mechanical interference effects, are reviewed in Chapter 5. The last two chapters are devoted to the two forms of perturbation—predissociation and autoionization. This publication is a good source for graduate students, theorists, experimentalists, and potential users of spectroscopic data.

Author : E.M. de Jager
Publisher : Elsevier
ISBN 13 : 9780080542751
Total Pages : 339 pages
Book Rating : 4.51/5 ( download)

DOWNLOAD NOW!

Download or read book The Theory of Singular Perturbations written by E.M. de Jager and published by Elsevier. This book was released on 1996-11-08 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathematical justification of these methods. The latter implies a priori estimates of solutions of differential equations; this involves the application of Gronwall's lemma, maximum principles, energy integrals, fixed point theorems and Gåding's theorem for general elliptic equations. These features make the book of value to mathematicians and researchers in the engineering sciences, interested in the mathematical justification of formal approximations of solutions of practical perturbation problems. The text is selfcontained and each chapter is concluded with some exercises.

Author : William McKnight Ritter
Publisher :
ISBN 13 :
Total Pages : 186 pages
Book Rating : 4.18/5 ( download)

DOWNLOAD NOW!

Download or read book A New Method of Determining the General Perturbations of the Minor Planets written by William McKnight Ritter and published by . This book was released on 1896 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Yifeng Xue
Publisher : World Scientific
ISBN 13 : 9814383600
Total Pages : 305 pages
Book Rating : 4.08/5 ( download)

DOWNLOAD NOW!

Download or read book Stable Perturbations of Operators and Related Topics written by Yifeng Xue and published by World Scientific. This book was released on 2012 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad introduction to the generalized inverses, MooreOCoPenrose inverses, Drazin inverses and TOCoS outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on. Stable Perturbations of Operators and Related Topics is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students. It is also suitable for researchers as a reference. The proofs of statements and explanations in the book are detailed enough that interested readers can study it by themselves."

Author : James G. Simmonds
Publisher : Courier Corporation
ISBN 13 : 0486315584
Total Pages : 162 pages
Book Rating : 4.84/5 ( download)

DOWNLOAD NOW!

Download or read book A First Look at Perturbation Theory written by James G. Simmonds and published by Courier Corporation. This book was released on 2013-07-04 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the approximate solution. Knowledge of perturbation theory offers a twofold benefit: approximate solutions often reveal the exact solution's essential dependence on specified parameters; also, some problems resistant to numerical solutions may yield to perturbation methods. In fact, numerical and perturbation methods can be combined in a complementary way. The text opens with a well-defined treatment of finding the roots of polynomials whose coefficients contain a small parameter. Proceeding to differential equations, the authors explain many techniques for handling perturbations that reorder the equations or involve an unbounded independent variable. Two disparate practical problems that can be solved efficiently with perturbation methods conclude the volume. Written in an informal style that moves from specific examples to general principles, this elementary text emphasizes the "why" along with the "how"; prerequisites include a knowledge of one-variable calculus and ordinary differential equations. This newly revised second edition features an additional appendix concerning the approximate evaluation of integrals.

Author : W. Eckhaus
Publisher : Elsevier
ISBN 13 : 9780080875309
Total Pages : 286 pages
Book Rating : 4.00/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Analysis of Singular Perturbations written by W. Eckhaus and published by Elsevier. This book was released on 2011-08-30 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Analysis of Singular Perturbations

Author : Richard Ernest Bellman
Publisher : Courier Corporation
ISBN 13 : 9780486432588
Total Pages : 146 pages
Book Rating : 4.80/5 ( download)

DOWNLOAD NOW!

Download or read book Perturbation Techniques in Mathematics, Engineering and Physics written by Richard Ernest Bellman and published by Courier Corporation. This book was released on 2003-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students receive a stimulating introduction to analytical approximation techniques for solving differential equations in this text, which introduces scientifically significant problems and indicates useful solutions. 1966 edition.