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Computational methods for modelling of nonlinear systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Computational methods for modelling of nonlinear systems/ A. Torokhti, P. Howlett.
remainder title:	Computational methods for modeling of nonlinear systems
Author:	Torokhti, A.
other author:	Howlett, P. G.
Published:	Amsterdam ;Elsevier, : 2007.,
Description:	xi, 397 p. :ill. (some col.) ; : 24 cm.;
Series:	Mathematics in science and engineering,
Subject:	Nonlinear systems - Mathematical models. -
Online resource:	An electronic book accessible through the World Wide Web; click for information
ISBN:	9780444530448

Computational methods for modelling of nonlinear systems
Torokhti, A.

Computational methods for modelling of nonlinear systems[electronic resource] /Computational methods for modeling of nonlinear systemsA. Torokhti, P. Howlett. - 1st ed. - Amsterdam ;Elsevier,2007. - xi, 397 p. :ill. (some col.) ;24 cm. - Mathematics in science and engineering,v. 2120076-5392 ;.

Includes bibliographical references (p. 379-393) and index.

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<P>.

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.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780444530448

Source: 136796:136930Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

264042
Nonlinear systems
--Mathematical models.Index Terms--Genre/Form:

96803
Electronic books.

LC Class. No.: QA427 / .T67 2007eb

Dewey Class. No.: 515.72480113

Computational methods for modelling of nonlinear systems
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260 $a Amsterdam ; $a Boston : $c 2007. $b Elsevier,
300 $a xi, 397 p. : $b ill. (some col.) ; $c 24 cm.
440 0 $a Mathematics in science and engineering, $x 0076-5392 ; $v v. 212
504 $a Includes bibliographical references (p. 379-393) and index.
505 0 $a 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<P>.
520 $a 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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