Comparison and Oscillation Theory of Linear Differential Equations by C A Swanson

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 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 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, n th 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 Sturm-type theorems for second order ordinary equations Oscillation and nonoscillation theorems for second order ordinary equarions Fourth order ordinary equations Third order ordinary equations, nth order ordinary equations and systems Partial differential equations.