Buch, Englisch, Band 74, 322 Seiten, Format (B × H): 152 mm x 229 mm
Buch, Englisch, Band 74, 322 Seiten, Format (B × H): 152 mm x 229 mm
Reihe: Mathematics in Science and Engineering
ISBN: 978-0-12-436650-3
Verlag: Elsevier Science & Technology
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
Zielgruppe
This book is intended for:
Applied mathematicians and Electrical engineers
And:
Statisticians
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Nichtlineare Wissenschaft
Weitere Infos & Material
Preface
Contents
1 Overview
I Methods of Operator Approximation in System Modelling
2 Nonlinear Operator Approximation with Preassigned Accuracy
2.1 Introduction
2.2 Generic formulation of the problem
2.3 Operator approximation in space C([0; 1]):
2.4 Operator approximation in Banach spaces by polynomial operators
2.5 Approximation on compact sets in topological vector spaces
2.6 Approximation on noncompact sets in Hilbert spaces
2.7 Special results for maps into Banach spaces
2.8 Concluding remarks
3 Interpolation of Nonlinear Operators 65
3.1 Introduction
3.2 Lagrange interpolation in Banach spaces
3.3 Weak interpolation of nonlinear operators
3.4 Some related results
3.5 Concluding remarks
4 Realistic Operators and their Approximation
4.1 Introduction
4.2 Formalization of concepts related to description of real-world objects
4.3 Approximation of R¡continuous operators
4.4 Concluding remarks
5 Methods of Best Approximation for Nonlinear Operators
5.1 Introduction
5.2 Best Approximation of nonlinear operators in Banach spaces: Deterministic case
5.3 Estimation of mean and covariance matrix for random vectors
5.4 Best Hadamard-quadratic approximation
5.5 Best polynomial approximation
5.6 Best causal approximation
5.7 Best hybrid approximations
5.8 Concluding remarks
II Optimal Estimation of Random Vectors
6 Computational Methods for Optimal Filtering of Stochastic Signals
6.1 Introduction
6.2 Optimal linear Filtering in Finite dimensional vector spaces
6.3 Optimal linear Filtering in Hilbert spaces
6.4 Optimal causal linear Filtering with piecewise constant memory
6.5 Optimal causal polynomial Filtering with arbitrarily variable memory
6.6 Optimal nonlinear Filtering with no memory constraint
6.7 Concluding remarks
7 Computational Methods for Optimal Compression and
Reconstruction of Random Data
7.1 Introduction
7.2 Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT)
7.3 Rank-constrained matrix approximations
7.4 Generic PCA{KLT
7.5 Optimal hybrid transform based on Hadamard-quadratic approximation
7.6 Optimal transform formed by a combination of nonlinear operators
7.7 Optimal generalized hybrid transform
7.8 Concluding remarks
Bibliography
Index