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Preface | |
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Overview | |
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Methods of Operator Approximation in System Modelling | |
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Nonlinear Operator Approximation with Preassigned Accuracy | |
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Introduction | |
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Generic formulation of the problem | |
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Operator approximation in space C([0; 1]) | |
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Operator approximation in Banach spaces by polynomial operators | |
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Approximation on compact sets in topological vector spaces | |
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Approximation on noncompact sets in Hilbert spaces | |
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Special results for maps into Banach spaces | |
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Concluding remarks | |
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Interpolation of Nonlinear Operators 65 | |
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Introduction | |
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Lagrange interpolation in Banach spaces | |
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Weak interpolation of nonlinear operators | |
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Some related results | |
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Concluding remarks | |
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Realistic Operators and their Approximation | |
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Introduction | |
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Formalization of concepts related to description of real-world objects | |
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Approximation of R��continuous operators | |
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Concluding remarks | |
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Methods of Best Approximation for Nonlinear Operators | |
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Introduction | |
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Best Approximation of nonlinear operators in Banach spaces: Deterministic case | |
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Estimation of mean and covariance matrix for random vectors | |
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Best Hadamard-quadratic approximation | |
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Best polynomial approximation | |
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Best causal approximation | |
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Best hybrid approximations | |
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Concluding remarks | |
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Optimal Estimation of Random Vectors | |
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Computational Methods for Optimal Filtering of Stochastic Signals | |
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Introduction | |
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Optimal linear Filtering in Finite dimensional vector spaces | |
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Optimal linear Filtering in Hilbert spaces | |
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Optimal causal linear Filtering with piecewise constant memory | |
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Optimal causal polynomial Filtering with arbitrarily variable memory | |
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Optimal nonlinear Filtering with no memory constraint | |
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Concluding remarks | |
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Computational Methods for Optimal Compression and Reconstruction of Random Data | |
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Introduction | |
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Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) | |
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Rank-constrained matrix approximations | |
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Generic PCA{KLT | |
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Optimal hybrid transform based on Hadamard-quadratic approximation | |
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Optimal transform formed by a combination of nonlinear operators | |
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Optimal generalized hybrid transform | |
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Concluding remarks | |
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Bibliography | |
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Index | |