روش‌های مقدار اولیه برای مسائل مرزی: نظریه و کاربرد جاسازی پایدار

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 Dedication Page v Preface Pages xi-xii Acknowlegments Page xiii Introduction Pages 1-8 Chapter 1 Characteristic Theory Pages 9-33 Chapter 2 Two-Point Boundary Value Problems Pages 34-104 Chapter 3 Interface Problems Pages 105-141 Chapter 4 Multipoint Boundary Value Problems Pages 142-164 Chapter 5 Invariant Imbedding for Abstract Equations Pages 165-197 Chapter 6 Infinite-Dimensional Riccati Equations Pages 198-211 References Pages 212-216 Index Pages 217-220 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.