Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding
( Volume 100 )
Publication series ：Volume 100
Publisher： Elsevier Science
Publication year： 1973
E-ISBN: 9780080956091
P-ISBN(Paperback): 9780124929500
P-ISBN(Hardback): 9780124929500
Subject： O15 algebra, number theory, combinatorial theory;O241 数值分析
Language： ENG
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Description
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
Chapter