Comparison and Oscillation Theory of Linear Differential Equations

✍ Scribed by C.A. Swanson (Eds.)

• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Leaves: 234
• Series: Mathematics in Science and Engineering 48
• 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

Content:
Edited by
Page iii

Copyright page
Page iv

Preface
Pages v-vi
C.A. Swanson

Chapter 1 Sturm-Type Theorems for Second Order Ordinary Equations
Pages 1-43

Chapter 2 Oscillation and Nonoscillation Theorems for Second Order Ordinary Equations
Pages 44-112

Chapter 3 Fourth Order Ordinary Equations
Pages 113-148

Chapter 4 Third Order Ordinary Equations, nth Order Ordinary Equations and Systems
Pages 149-185

Chapter 5 Partial Differential Equations
Pages 186-212

Bibliography Review Article
Pages 213-222

Author Index
Pages 223-225

Subject Index
Pages 226-227