Computational Methods for Modeling of Nonlinear Systems, Volume 127 (Mathematics in Science and Engineering)

✍ Scribed by Anatoli Torokhti, Phil Howlett

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Leaves: 343
• Category: Library

✦ 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

✦ Table of Contents

Singular and Degenerate Cauchy Problems
Copyright Page
Contents
Preface
Chapter 1. Singular Partial Differential Equations of EPD Type
1.1. Examples
1.2. Mean values in Rn
1.3. The Fourier method
1.4. Connection formulas and properties of solutions for EPD equations in D' and S'
1.5. Spectral techniques and energy methods in Hilbert space
1.6. EPD equations in general spaces
1.7. Transmutation
Chapter 2. Canonical Sequences of Singular Cauchy Problems
2.1. The rank one situation
2.2. Resolvants

2.4. Expressions for general resolvants
2.5. The Euclidean case plus generalizations
Chapter 3. Degenerate Equations with Operator Coefficients
3.1. Introduction
3.2. The Cauchy problem by spectral techniques
3.3. Strongly regular equations
3.4. Weakly regular equations
3.5. Linear degenerate equations
3.6. Semilinear degenerate equations
3.7. Doubly nonlinear equations
Chapter 4. Selected Topics
4.1. Introduction
4.2. Huygens' principle
4.3. The generalized radiation problem of Weinstein
4.4. Improperly posed problems
4.5. Miscellaneous problems
REFERENCES
INDEX