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Media type:
E-Book
Title:
Some successive approximation methods in control and oscillation theory
Contains:
Front Cover; Some Successive Approximation Methods in Control and Oscillation Theory; Copyright Page; Preface; CONTENTS; CHAPTER 1. INTRODUCTlON; 1.1 Introduction; 1.2 Control Problems and Historical Notes; 1.3 Description of Contents; CHAPTER 2. OPERATOR THEORETIC ITERATIVE METHODS; 2.1 Introduction; 2.2 The Method of Contraction Mappings; 2.3 The Modified Contraction Mapping Method; 2.4 Newton's Method; 2.5 Multipoint Methods; CHAPTER 3. REPRESENTATION OF BOUNDARY VALUE PROBLEMS; 3.1 lntroduction; 3.2 Continuous Linear Two-Point Boundary Value Problems
3.3 Discrete Linear Two-Point Boundary Value Problems3.4 Representation of Continuous Two-Point Boundary Value Problems; 3.5 Representation of Discrete Two-Point Boundary Value Problem; 3.6 A Continuous Example; 3.7 A Discrete Example; 3.8 Computation of Derivatives: Continuous Case; 3.9 Computation of Derivatives: Discrete Case; 3.10 A Lemma on Equivalence: Continuous Case; 3.11 A Lemma on Equivalence: Discrete Case; Appendix. Lipschitz Norms; CHAPTER 4. APPLICATION TO CONTROL PROBLEMS; 4.1 Introduction; 4.2 Continuous Control Problems; 4.3 A Continuous Example; 4.4 Discrete Control Problems
4.5 Application to Continuous Problems I: The Method of Contraction Mappings4.6 Application to Continuous Problems II: The Modified Contraction Mapping Method; 4.7 Application to Continuous Problems III: Newton's Method; 4.8 Application to Continuous Problems IV: Multipoint Methods; 4.9 Application to Discrete Problems I: The Method of Contraction Mappings; 4.10 Application to Discrete Problems II: The Modified Contraction Mapping Method; 4.11 Application to Discrete Problems III: Newton's Method; 4.12 Summary; CHAPTER 5. APPLICATION TO OSCILLATION PROBLEMS; 5.1 Introduction
5.2 Almost Linear Problems5.3 Some Second-Order Examples; CHAPTER 6. SOME NUMERICAL EXAMPLES; 6.1 Introduction; 6.2 Constant Low-Thrust Earth-to-Mars Orbital Transfer; 6.3 Variable Low-Thrust Earth-to-Mars Orbital Transfer; 6.4 An Oscillation Problem; REFERENCES; AUTHOR INDEX; SUBJECT INDEX; Mathematics in Science and Engineering;
Place of reproduction:
[S.l.]: HathiTrust Digital Library
Reproduction note:
Online-Ausg. [S.l.] : HathiTrust Digital Library
Origination:
Footnote:
Includes bibliographical references and index. - Print version record
Print version record
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002
Description:
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