| Edition |
1st ed. |
| Description |
1 online resource (xi, 397 pages) : illustrations (some color) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Mathematics in science and engineering, 0076-5392 ; v. 212 |
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Mathematics in science and engineering ; v. 212. 0076-5392
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| Summary |
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. |
| Contents |
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 RLcontinuous 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. |
| Bibliography |
Includes bibliographical references (pages 379-393) and index. |
| Note |
Print version record. |
| Subject |
Nonlinear systems -- Mathematical models.
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System theory.
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Systems Theory |
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Systèmes non linéaires -- Modèles mathématiques.
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Théorie des systèmes.
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MATHEMATICS -- Functional Analysis.
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Nonlinear systems -- Mathematical models
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Niet-lineaire systemen.
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Optimaliseren.
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| Genre/Form |
dissertations.
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Academic theses
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Academic theses.
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Thèses et écrits académiques.
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| Added Author |
Howlett, P. G. (Philip G.), 1944-
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| Added Title |
Computational methods for modeling of nonlinear systems |
| Other Form: |
Print version: Torokhti, A. (Anatoli). Computational methods for modelling of nonlinear systems. 1st ed. Amsterdam ; Boston : Elsevier, 2007 9780444530448 0444530444 (OCoLC)123111879 |
| ISBN |
9780080475387 (electronic bk.) |
|
0080475388 (electronic bk.) |
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9786611003906 |
|
6611003908 |
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9780444530448 |
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0444530444 |
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9780750668477 |
| Standard No. |
AU@ 000048129815 |
|
AU@ 000051561134 |
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AU@ 000059268295 |
|
CHNEW 001006086 |
|
DEBBG BV036962191 |
|
DEBBG BV039834072 |
|
DEBBG BV042317172 |
|
DEBBG BV043043927 |
|
DEBSZ 276084985 |
|
DEBSZ 42220367X |
|
DEBSZ 482354178 |
|
NZ1 11778355 |
|
NZ1 14540161 |
|
NZ1 15192401 |
|
UKMGB 017581677 |
|
