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