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 Content: Edited by Page iii Copyright page Page iv Preface Pages ix-x Translator's Note Page x Introduction Pages xi-xii 1 Elements of Mathematical Logic Pages 1-26 2 Engineering Applications of Propositional Calculus Pages 27-57 3 Finite Automata and Sequential Machines: Basic Concepts Pages 58-85 4 Abstract Structure and Nets Pages 86-115 5 Technical Embodiment of Finite Automata and Sequential Machines Pages 116-143 6 Autonomous Finite Automata and Sequential Machines Pages 144-158 7 Representation of Events in Finite Automata and Sequential Machines Pages 159-186 8 Recognition of Realizability of a Given Specification. Abstract Synthesis of Finite Automata and Sequential Machines Pages 187-218 9 Equivalence and Minimization of Sequential Machines Pages 219-259 10 Transformation of Clock Rates of Sequential Machines Pages 260-283 11 Determination of the Properties of Sequential Machines from Their Response to Finite Input Sequences Pages 284-303 12 Algorithms Pages 304-354 13 Turing Machines Pages 355-376 Conclusion Pages 377-385 Problems Pages 386-408 Bibliography Review Article Pages 409-426 Addenda to Bibliography Review Article Pages 427-429 Index Pages 430-433 Studies theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. This title considers many computing techniques, such as methods of operator approximation with any given accuracy; methods of covariance matrix estimation; and, methods for low-rank matrix approximations.
