Quadratic form theory and differential equations /
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-Lagrang...
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Main Authors: | |
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Corporate Authors: | |
Published: |
Academic Press,
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Publisher Address: | New York : |
Publication Dates: | 1980. |
Literature type: | eBook |
Language: | English |
Series: |
Mathematics in science and engineering ;
v. 152 |
Subjects: | |
Online Access: |
http://www.sciencedirect.com/science/bookseries/00765392/152 |
Summary: |
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. |
Carrier Form: | 1 online resource (xii, 237 pages) : illustrations. |
Bibliography: | Includes bibliographical references (pages 231-233) and index. |
ISBN: |
9780080956602 0080956602 9780123014504 0123014506 |
Index Number: | QA243 |
CLC: | O156.5 |
Contents: |
Front Cover; Quadratic Form Theory and Differential Equations; Copyright Page; Contents; Preface; Chapter 0 A Few Introductory Remarks; Chapter 1 Introduction to Quadratic Forms and Differential Equations; 1.0 Introduction; 1.1 The Finite-Dimensional Case; 1.2 The Calculus of Variations; 1.3 Fundamental Lemmas (Integration by Parts); 1.4 Quadratic Forms and Differential Equations; Chapter 2 Abstract Theory; 2.0 Introduction; 2.1 Hilbert Space Theory; 2.2 Further Ideas of Hestenes; 2.3 Approximation Theory of Quadratic Forms; Chapter 3 The Second-Order Problem; 3.0 Introduction. 3.1 The Focal-Point Problem3.2 The Numerical Problem; 3.3 The Eigenvalue Problem; 3.4 The Numerical Eigenvalue Problems; 3.5 Proofs of Results; Chapter 4 The 2nth-Order Problem; 4.0 Introduction; 4.1 The Signature Theory of Lopez; 4.2 Approximation Theory; 4.3 Comparison Results; 4.4 Higher-Order Numerical Problems and Splines; Chapter 5 Elliptic Partial Differential Equations; 5.0 Introduction; 5.1 Summary; 5.2 The Numerical Problem; 5.3 Separation of Variables; Chapter 6 The Quadratic Control Problem; 6.0 Introduction; 6.1 Focal-Interval Theory of Quadratic Forms. 6.2 Focal Arcs of Differential Equations6.3 Two Examples; 6.4 An Approximation Theory of Focal Intervals; Postscript The Numerical Problem Revisited; 1. The x(t)x'(t) Term; 2. Cheap Boundary- Value Methods; 3. Systems; 4. Nonlinear Problems; References; Index. |