Format:
Online Ressource (ix, 339 pages)
,
illustrations.
Edition:
Online-Ausg. [S.l.] HathiTrust Digital Library Online-Ausg. [S.l.] : HathiTrust Digital Library
ISBN:
9780080956411
,
0080956416
,
9780121962500
Series Statement:
Mathematics in science and engineering v. 132
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
,
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; Functional Analysis in Modern Applied Mathematics; Copyright Page; Contents; Introduction; PART I: Basic Functional Analysis; Chapter 1. NORMED LINEAR SPACES; Chapter 2. INTEGRATION THEORY FOR REAL-VALUED FUNCTIONS; Chapter 3. LINEAR TRANSFORMATIONS; Chapter 4. HILBERT SPACES; Chapter 5. PROBABILITY THEORY; Chapter 6. CALCULUS IN BANACH SPACES; Chapter 7. TOPOLOGICAL SPACES; Part II: Analysis of Abstract Equations; Chapter 8. DIFFERENTIAL EQUATIONS; 8.1 Ordinary differential equations; 8.2 Stochastic differential equations; 8.3 Differential delay equations
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8.4 Partial differential equations8.5 Abstract equations; 8.6 Semigroup theory; 8.7 Solution of inhomogeneous abstract evolution equations; Chapter 9. SPECTRAL THEORY AND APPLICATIONS; 9.1 Spectral theory in finite dimensions; 9.2 Spectrum of closed linear operators on a normed linear space; 9.3 Spectral theory for compact normal operators; 9.4 Spectral decomposition for unbounded linear operators; Part III: Applications; Chapter 10. STABILITY THEORY; 10.1 Liapunov stability for ordinary differential equations; 10.2 Stability properties of operators : perturbation theory
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Chapter 11. LINEAR SYSTEMS THEORY11.1 Controllability; 11.2 Stability; 11.3 Observability; 11.4 Linear quadratic control problems; 11.5 Filtering; 11.6 Time optimal control; Chapter 12. OPTIMIZATION PROBLEMS; 12.1 Minimization of coercive bilinear forms; 12.2 Least squares minimization in a Hilbert space; 12.3 Unconstrained Calculus of Variations problems; 12.4 Minimization under equality constraints; 12.5 Minimization with inequality constraints; 12.6 Optimal control theory; Chapter 13. NUMERICAL METHODS; 13.1 General principles and introduction; 13.2 Linear equations
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13.3 Nonlinear equations13.4 Approximation theory; 13.5 Numerical solution of optimization problems; Chapter 14. INFINITE DIMENSIONAL LINEAR SYSTEMS THEORY; 14.1 Controllability; 14.2 Observability; 14.3 The quadratic cost control problem for evolution equations; 14.4 A direct approach to the quadratic cost control problem; INDEX
,
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 0121962504
Additional Edition:
Erscheint auch als Druck-Ausgabe Curtain, Ruth F Functional analysis in modern applied mathematics London ; New York : Academic Press, 1977
Language:
English
Keywords:
Electronic books
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Electronic books
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Electronic resource
