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Functional analysis in modern applied mathematics / Ruth F. Curtain, A.J. Pritchard

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Mathematics in science and engineering ; v. 132Publisher: London ; New York : Academic Press, 2010Description: Online Ressource (ix, 339 pages) : illustrationsISBN:
  • 9780121962500
  • 9780080956411
  • 0080956416
  • 0121962504
  • 9780121962500
Subject(s): Additional physical formats: 0121962504 | Erscheint auch als: Functional analysis in modern applied mathematics. Druck-Ausgabe London ; New York : Academic Press, 1977DDC classification:
  • 515.7
LOC classification:
  • QA320
Online resources: Additional physical formats: Online-Ausg. [S.l.] : HathiTrust Digital Library
Contents:
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
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
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
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
Summary: 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 compressionPPN: PPN: 878888292Package identifier: Produktsigel: BSZ-33-EBS-C1UB | BSZ-33-EBS-HSAA | GBV-33-EBS-MRI | GBV-33-EBS-ZHB | GBV-33-Freedom-BL | ZDB-1-ELC | ZDB-33-EBS | ZDB-33-ESD
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Online-Ausg. [S.l.] : HathiTrust Digital Library

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

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