Computational methods for modelling of nonlinear systems. (2007)

• Record Type: Book
• Other Titles: Computational methods for modeling of nonlinear systems
• Further Information: Note: A. Torokhti, P. Howlett.
• Other Names: Torokhti, A (Anatoli); Howlett, P. G (Philip G.), 1944-
• 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 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.
• Publisher Details: Amsterdam Boston : Elsevier
• Publication Date: 2007
• Extent: 1 online resource (xi, 397 pages), illustrations (some color)
• Subjects: 515.72480113; Nonlinear systems -- Mathematical models; Sistemas no lineales -- Modelos matemáticos; MATHEMATICS -- Functional Analysis; Nonlinear systems -- Mathematical models; Niet-lineaire systemen; Optimaliseren; Electronic books
• Languages: English
• ISBNs: 9780080475387; 0080475388; 9786611003906; 6611003908
• Related ISBNs: 9780444530448; 0444530444; 9780750668477
• Notes: Note: Includes bibliographical references (pages 379-393) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.