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Computational methods for modelling of nonlinear systems /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Elsevier,
2007.
|
| Edición: | 1st ed. |
| Colección: | Mathematics in science and engineering ;
v. 212. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Torokhti, A. |q (Anatoli) | |
| 245 | 1 | 0 | |a Computational methods for modelling of nonlinear systems / |c A. Torokhti, P. Howlett. |
| 246 | 3 | |a Computational methods for modeling of nonlinear systems | |
| 250 | |a 1st ed. | ||
| 260 | |a Amsterdam ; |a Boston : |b Elsevier, |c 2007. | ||
| 300 | |a 1 online resource (xi, 397 pages) : |b illustrations (some color) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics in science and engineering, |x 0076-5392 ; |v v. 212 | |
| 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. | ||
| 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 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. | |
| 504 | |a Includes bibliographical references (pages 379-393) and index. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Nonlinear systems |x Mathematical models. | |
| 650 | 6 | |a Systèmes non linéaires |x Modèles mathématiques. | |
| 650 | 7 | |a MATHEMATICS |x Functional Analysis. |2 bisacsh | |
| 650 | 7 | |a Nonlinear systems |x Mathematical models. |2 fast |0 (OCoLC)fst01038811 | |
| 650 | 1 | 7 | |a Niet-lineaire systemen. |2 gtt |
| 650 | 1 | 7 | |a Optimaliseren. |2 gtt |
| 700 | 1 | |a Howlett, P. G. |q (Philip G.), |d 1944- | |
| 776 | 0 | 8 | |i Print version: |a Torokhti, A. (Anatoli). |t Computational methods for modelling of nonlinear systems. |b 1st ed. |d Amsterdam ; Boston : Elsevier, 2007 |z 9780444530448 |z 0444530444 |w (OCoLC)123111879 |
| 830 | 0 | |a Mathematics in science and engineering ; |v v. 212. |x 0076-5392 | |
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