Computational Methods for Modelling of Nonlinear Systems

A. Torokhti and P. Howlett (Eds.)9780444530448, 0444530444

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

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Table of contents :
Content:
Preface
Pages vii-viii

Chapter 1 Overview
Pages 1-6

Chapter 2 Nonlinear operator approximation with preassigned accuracy Original Research Article
Pages 9-63

Chapter 3 Interpolation of nonlinear operators Original Research Article
Pages 65-95

Chapter 4 Realistic operators and their approximation Original Research Article
Pages 97-135

Chapter 5 Methods of best approximation for nonlinear operators Original Research Article
Pages 137-225

Chapter 6 Computational methods for optimal filtering of stochastic signals Original Research Article
Pages 229-290

Chapter 7 Computational methods for optimal compression and reconstruction of random data Original Research Article
Pages 291-378

Bibliography Original Research Article
Pages 379-393

Index
Pages 395-397