Computational methods for modelling of nonlinear systems
Record details
- ISBN: 9780444530448
- ISBN: 0444530444
- ISBN: 9780080475387 (electronic bk.)
- ISBN: 0080475388 (electronic bk.)
- ISBN: 9780750668477
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Physical Description:
electronic resource
remote
1 online resource (xi, 397 p.) : ill. (some col.) - Edition: 1st ed.
- Publisher: Amsterdam ; Boston : Elsevier, 2007.
Content descriptions
General Note: | CatMonthString:jan.13 Multi-User. CatBulkString:jan.03.13 |
Bibliography, etc. Note: | Includes bibliographical references (p. 379-393) and index. |
Formatted Contents Note: | 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 RŁcontinuous 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 . |
Source of Description Note: | Description based on print version record. |
Search for related items by subject
Subject: | Nonlinear systems -- Mathematical models Nonlinear systems -- Mathematical models Niet-lineaire systemen Optimaliseren MATHEMATICS -- Functional Analysis |
Genre: | Electronic books. |