Keith B. Oldham and Jerome Spanier (Eds.)9780125255509, 9780486450018, 0125255500, 0486450015
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 |
Table of contents :
Content:
Edited by
Page iii Copyright page
Page iv Preface
Pages ix-xii Acknowledgments
Page xiii Chapter 1: Introduction
Pages 1-24 Chapter 2: Differentiation and Integration to Integer Order
Pages 25-44 Chapter 3: Fractional Derivatives and Integrals: Definitions and Equivalences
Pages 45-60 Chapter 4: Differintegration of Simple Functions
Pages 61-68 Chapter 5: General Properties
Pages 69-91 Chapter 6: Differintegration of More Complex Functions
Pages 93-113 Chapter 7: Semiderivatives and Semiintegrals
Pages 115-131 Chapter 8: Techniques in the Fractional Calculus
Pages 133-160 Chapter 9: Representation of Transcendental Functions
Pages 161-180 Chapter 10: Applications in the Classical Calculus
Pages 181-195 Chapter 11: Applications to Diffusion Problems
Pages 197-218 References
Pages 219-223 Index
Pages 225-234 |
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