The Padé approximant in theoretical physics

Medientyp: E-Book

Titel: The Padé approximant in theoretical physics

Enthält: Front Cover; The Padé Approximant in Theoretical Physics; Copyright Page; Contents; List of Contributors; Preface; Chapter 1. The Padé Approximant Method and Some Related Generalizations; I. Introduction; II. The Theory of the Padé Approximant Method; III. Generalized Approximation Procedures; IV. Applications; References; Chapter 2. Application of Padé Approximants to Dispersion Force and Optical Polarizability Computations; I. Introduction; II. Formalism; III. Computation Procedures; IV. Applications; V. Comparisions with Related Methods; VI. Concluding Remarks; References
Chapter 3. Bounds for Averages Using Moment ConstraintsI. Introduction; II. The Moments Problem; III. Applications; IV. Conclusion; Appendix A; Appendix B; References; Chapter 4. Turbulent Diffusion: Evaluation of Primitive and Renormalized Perturbation Series by Padé Approximants and by Expansion of Stieltjes Transforms into Contributions from Continuous Orthogonal Functions; I. Introduction; II. Continuous Orthogonal Expansion of Stieltjes Transforms; III. Examples Comparing Continuous Orthogonal Expansion and Padé Approximants; IV. Diffusion by a Random Velocity Field
V. Perturbation Expansions for the Diffusion ProblemVI. Approximants to the Primitive Perturbation Expansions; VII. Approximants to the Irreducible Expansion References; References; Chapter 5. Padé Approximants and Linear Integral Equations; I. Introduction; II. Properties of Linear Integral Equations; III. Integral Equations and Padé Approximants; IV. The Integral Equation for Potential Scattering References; References; Chapter 6. Series of Derivatives of d-Functions; I. Introduction; II. An Example; III. Expressions for g(k); IV. Approximants to g(k); V. Conclusions; References
Chapter 7. Hilbert Space and the Padé ApproximantI. Introduction; II. Extended Series of Stieltjes; III. Symmetric Operators and the Padé Approximant; IV. Method of Moments; V. Discussion; References; Chapter 8. The Connection of Padé Approximants with Stationary Variational Principles and the Convergence of Certain Padé Approximants; I. Introduction; II. Derivation of Padé Approximants from Stationary Variational Principles; III. Convergence of Padé Approximants; IV. The Convergence of Padé Approximants to Convergent Power Series; References
Chapter 9. Approximate N/D Solutions Using Padé ApproximantsI. Introduction; II. Method; III. Proof of Unitarity and Convergence; IV. Discussion; References; Chapter 10. The Solution of the N/D Equations Using the Padé Approximant Method; I. Introduction; II. The Integral Equations for Nand D and Their Approximate Solution; III. Convergent Sequences of Approximate Solutions to the N/D Equations; IV. The ? Bootstrap and Related Amplitudes; References; Chpater 11. Padé Approximants as a Computational Tool for Solving the Schrödinger and Bethe-Salpeter Equations; I. Introduction
II. Basic Philosophy and a Simple Example

Beteiligte: Gammel, John L. [Sonstige Person, Familie und Körperschaft]; Baker, George A. [Sonstige Person, Familie und Körperschaft]

Erschienen: New York: Academic Press, 2010
Online-Ausg.: [S.l.]: HathiTrust Digital Library

Umfang: Online Ressource (xii, 378 pages); illustrations

Sprache: Englisch

ISBN: 9780080955803; 0080955800; 9780120748501

RVK-Notation: SK 470 : Reihen, Folgen, Approximationstheorie,

Schlagwörter: Physique mathématique ; Padé, Approximation de ; Mathematical physics ; Padé approximant ; Pade§ approximant ; Physics ; Science ; Pade approximant ; Padé-Näherung ; Padé-Näherungsbruch ; Theoretische Physik ; Padé-benaderingen ; Natuurkunde ; Aproximacao (Analise Numerica) ; SCIENCE ; Physics ; Mathematical & Computational ; Padé, Approximants de ; Electronic books

Art der Reproduktion: Online-Ausg.

Hersteller der Reproduktion: [S.l.]: HathiTrust Digital Library

Reproduktionsnotiz: Online-Ausg. [S.l.] : HathiTrust Digital Library

Entstehung:

Anmerkungen: Includes bibliographical references and index. - Print version record
Print version record
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002

Beschreibung: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression

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