Functional Analysis In Modern Applied Mathematics
by Ruth F Curtain /
1977 / English / PDF
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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
