Functional analysis in modern applied mathematics - Curtain, Ruth F.; Pritchard, A. J.; ScienceDirect eBooks (London ; New York : Academic Press, 1977)
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.
Cover13; -- 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 equations -- 8.5 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 THEORY -- 11.1 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 equations -- 13.4 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.
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Keywords: Functional analysis; MATHEMATICS -- Functional Analysis; Functional analysis; Analytische ruimten; Functionaalanalyse; Analyse fonctionnelle; Electronic books