Format:
Online Ressource (xii, 378 pages)
,
illustrations.
Edition:
Online-Ausg. [S.l.] HathiTrust Digital Library Online-Ausg. [S.l.] : HathiTrust Digital Library
ISBN:
9780080955803
,
0080955800
,
9780120748501
Series Statement:
Mathematics in science and engineering v. 71
Content:
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;〈BR id="CRLF"〉methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and〈BR id="CRLF"〉methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.〈BR id="CRLF"〉〈BR id="CRLF"〉As a result, the book represents a blend of new methods in general computational analysis, 〈BR id="CRLF"〉and specific, but also generic, techniques for study of systems theory ant its particular〈BR id="CRLF"〉branches, such as optimal filtering and information compression
Note:
Includes bibliographical references and index. - Print version record
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Print version record
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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
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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
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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
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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
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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
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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
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II. Basic Philosophy and a Simple Example
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Online-Ausg. [S.l.] : HathiTrust Digital Library
,
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.
Additional Edition:
ISBN 0120748509
Additional Edition:
Erscheint auch als Druck-Ausgabe Padé approximant in theoretical physics New York, Academic Press, 1970
Language:
English
Subjects:
Mathematics
Keywords:
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