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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 | |