Theory of Optimal Search (Mathematics in Science and Engineering)

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 Lawrence D. Stone Acknowledgments Pages xiii-xiv Introduction Pages 1-16 Chapter I Search Model Pages 17-34 Chapter II Uniformly Optimal Search Plans Pages 35-83 Chapter III Properties of Optimal Search Plans Pages 84-100 Chapter IV Search with Discrete Effort Pages 101-117 Chapter V Optimal Search and Stop Pages 118-135 Chapter VI Search in the Presence of False Targets Pages 136-178 Chapter VII Approximation of Optimal Plans Pages 179-196 Chapter VIII Conditionally Deterministic Target Motion Pages 197-220 Chapter IX Markovian Target Motion Pages 221-233 Appendix A Reference Theorems Pages 235-236 Appendix B Necessary Conditions for Constrained Optimization of Separable Functionals Pages 237-244 References Review Article Pages 245-249 Author Index Pages 251-253 Subject Index Pages 255-258 Notation Index Pages 259-260 Studies theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. This title also considers computing techniques, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; and, methods of covariance matrix estimation.