Stability and periodic solutions of ordinary and functional differential equations /
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| Author / Creator: | Burton, T. A. (Theodore Allen), 1935- |
|---|---|
| Imprint: | Orlando : Academic Press, 1985. |
| Description: | x, 337 p. : ill., port. ; 24 cm. |
| Language: | English |
| Series: | Mathematics in science and engineering v. 178 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/748502 |
Table of Contents:
- Preface
- 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 RÂícontinuous 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
