Computational methods for modelling of nonlinear systems /

Mostrar otras versiones (1)

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-Lagrang...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Torokhti, A. (Anatoli)
Otros Autores: Howlett, P. G. (Philip G.), 1944-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; Boston : Elsevier, 2007.
Edición:1st ed.
Colección:Mathematics in science and engineering ; v. 212.
Temas:
Nonlinear systems > Mathematical models.
Syst�emes non lin�eaires > Mod�eles math�ematiques.
MATHEMATICS > Functional Analysis.
Nonlinear systems > Mathematical models
Niet-lineaire systemen.
Optimaliseren.
Acceso en línea:Texto completo
Texto completo
Texto completo
Tabla de Contenidos:
  • Preface
  • Contents
  • 1 Overview
  • I Methods of Operator Approximation in System Modelling
  • 2 Nonlinear Operator Approximation with Preassigned Accuracy
  • 2.1 Introduction
  • 2.2 Generic formulation of the problem
  • 2.3 Operator approximation in space C([0; 1]):
  • 2.4 Operator approximation in Banach spaces by polynomial operators
  • 2.5 Approximation on compact sets in topological vector spaces
  • 2.6 Approximation on noncompact sets in Hilbert spaces
  • 2.7 Special results for maps into Banach spaces
  • 2.8 Concluding remarks
  • 3 Interpolation of Nonlinear Operators 65
  • 3.1 Introduction
  • 3.2 Lagrange interpolation in Banach spaces
  • 3.3 Weak interpolation of nonlinear operators
  • 3.4 Some related results
  • 3.5 Concluding remarks
  • 4 Realistic Operators and their Approximation
  • 4.1 Introduction
  • 4.2 Formalization of concepts related to description of real-world objects
  • 4.3 Approximation of R�continuous operators
  • 4.4 Concluding remarks
  • 5 Methods of Best Approximation for Nonlinear Operators
  • 5.1 Introduction
  • 5.2 Best Approximation of nonlinear operators in Banach spaces: Deterministic case
  • 5.3 Estimation of mean and covariance matrix for random vectors
  • 5.4 Best Hadamard-quadratic approximation
  • 5.5 Best polynomial approximation
  • 5.6 Best causal approximation
  • 5.7 Best hybrid approximations
  • 5.8 Concluding remarks
  • II Optimal Estimation of Random Vectors
  • 6 Computational Methods for Optimal Filtering of Stochastic Signals
  • 6.1 Introduction
  • 6.2 Optimal linear Filtering in Finite dimensional vector spaces
  • 6.3 Optimal linear Filtering in Hilbert spaces
  • 6.4 Optimal causal linear Filtering with piecewise constant memory
  • 6.5 Optimal causal polynomial Filtering with arbitrarily variable memory
  • 6.6 Optimal nonlinear Filtering with no memory constraint
  • 6.7 Concluding remarks
  • 7 Computational Methods for Optimal Compression and
  • Reconstruction of Random Data
  • 7.1 Introduction
  • 7.2 Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT)
  • 7.3 Rank-constrained matrix approximations
  • 7.4 Generic PCA{KLT
  • 7.5 Optimal hybrid transform based on Hadamard-quadratic approximation
  • 7.6 Optimal transform formed by a combination of nonlinear operators
  • 7.7 Optimal generalized hybrid transform
  • 7.8 Concluding remarks
  • Bibliography
  • Index.

Ejemplares similares