Front Cover -- Computational Methods for Modelling of Nonlinear Systems -- Copyright Page -- Preface -- Table of Contents -- Chapter 1 Overview -- Part I Methods of Operator Approximation in System Modelling -- Chapter 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 Operator Polynomials -- 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 -- Chapter 3 Interpolation of Nonlinear Operators -- 3.1 Introduction -- 3.2 Lagrange Interpolation in Banach Spaces -- 3.3 Weak Interpolation of Nonlinear Operators -- 3.4 Strong interpolation -- 3.5 Interpolation and approximation -- 3.6 Some Related Results -- 3.7 Concluding Remarks -- Chapter 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 R-continuous Operators -- 4.4 Concluding Remarks -- Chapter 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 r-Degree Polynomial Approximation -- 5.6 Best Causal Approximation -- 5.7 Best Hybrid Approximations -- 5.8 Concluding Remarks -- Part II Optimal Estimation of Random Vectors -- Chapter 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 -- Chapter 7 Computational Methods for Optimal Compression and Reconstruction of Random Data -- 7.1 Introduction -- 7.2 Standard Principal Component Analysis and Karhunen-Loève Transform (PCA-KLT) -- 7.3 Rank-constrained Matrix Approximations -- 7.4 A Generic Principal Component Analysis and Karhunen-Loève Transform -- 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 -- Series Page.