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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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Bibliographic Details
Main Authors: Gregory, John, 1938 March 2
Corporate Authors: Elsevier Science & Technology
Published: Academic Press,
Publisher Address: New York :
Publication Dates: 1980.
Literature type: eBook
Language: English
Series: Mathematics in science and engineering ; v. 152
Subjects:
Forms, Quadratic
Differential equations, Partial
Calculus of variations
Formes quadratiques
E quations aux de rive es partielles
Calcul des variations
MATHEMATICS > Algebra > Intermediate
Equacoes Diferenciais Ordinarias
Electronic books
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.

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