Items related to Theory of Difference Equations Numerical Methods and...
Synopsis
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
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Review
"[F]or the reader who is not familiar with the theory of difference equations [this book] represents a good introduction into the problem." - Mathematica Bohemica "The book has now been thoroughly revised and two new chapters added, which increases the value of the book considerably. [It] is clearly written, contains important results on linear as well as nonlinear equations and has many solved exercises. This new edition should have a place on the bookshelf of everyone working in this area. It is also suited for an advanced course on difference equations." - Mathematical Reviews, Issue 2004g "There are several books on integral operators in Orlicz spaces and some shorter expositions in several well-known monographs. An immense amount of material is scattered in a huge number of papers. [This book] fills this gap in important areas . The book will be very useful both for experts and students. It has been written by experienced authors and has been prepared with great skill." - Mathematica Bohemica
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