Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante

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 Chapter 1 Preliminaries Pages 1-25 Chapter 2 Linear Difference Equations Pages 27-61 Chapter 3 Linear Systems of Difference Equations Pages 63-85 Chapter 4 Stability Theory Pages 87-125 Chapter 5 Applications to Numerical Analysis Pages 127-153 Chapter 6 Numerical Methods for Differential Equations Pages 155-173 Chapter 7 Models of Real World Phenomena Pages 175-194 Appendix A Pages 195-210 Appendix B The Schur Criterium Pages 211-212 Appendix C Chebyshev Polynomials Pages 213-215 Solutions to the Problems Pages 217-230 References Pages 231-237 Subject Index Pages 239-242 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.