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Methods of Nonlinear Analysis

Autorzy: Richard Bellman Wydawnictwo: Elsevier Science Data wydania: 1970 Język publikacji: Angielski Liczba stron: 365 Formaty publikacji: EAN: 9780080955704 ISBN: 9780080955704 Kategoria: Numerical analysis Kolekcja specjalna: Rok matematyki 2019 Indeks wydawcy: S0076-5392(08)X6028-X Nota bibliograficzna: -


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.

- Best operator approximation,
- Non-Lagrange interpolation,
- Generic Karhunen-Loeve transform
- Generalised low-rank matrix approximation
- Optimal data compression
- Optimal nonlinear filtering

Spis treści

  • Front Cover 2
  • Methods of Nonlinear Analysis 5
  • Copyright Page 6
  • Preface 9
  • Contents 17
  • Chapter 1. First- and Second-order Differential Equations 25
    • 1.1. Introduction 25
    • 1.2. The First-order Linear Differential Equation 26
    • 1.3. Fundamental Inequality 27
    • 1.4. Second-order Linear Differential Equations 29
    • 1.5. Inhomogeneous Equation 31
    • 1.6. Lagrange Variation of Parameters 32
    • 1.7. Two-point Boundary Value Problem 34
    • 1.8. Connection with Calculus of Variations 35
    • 1.9. Green’s Functions 36
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