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
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I Methods of Operator Approximation in System Modelling 2. Nonlinear Operator Approximation with Preassigned Accuracy 3. Interpolation of Nonlinear Operators 65 4. Realistic Operators and their Approximation 5. Methods of Best Approximation for Nonlinear Operators
II Optimal Estimation of Random Vectors 6. Computational Methods for Optimal Filtering of Stochastic Signals 7. Computational Methods for Optimal Compression and Reconstruction of Random Data