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Discrete Hamiltonian Systems

Difference Equations, Continued Fractions, and Riccati Equations

  • Calvin D. Ahlbrandt
  • Allan C. Peterson

Part of the Kluwer Texts in the Mathematical Sciences book series (TMS, volume 16)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 1-44
  3. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 45-69
  4. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 71-151
  5. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 153-197
  6. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 199-262
  7. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 263-294
  8. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 295-317
  9. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 319-330
  10. Calvin D. Ahlbrandt, Allan C. Peterson
    Pages 331-356
  11. Back Matter
    Pages 357-375

About this book

Introduction

This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be used at the senior undergraduate level or beginning graduate level. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material. Continued fractions provide closed form representations of the extreme solutions of some discrete matrix Riccati equations. Continued fractions solution methods for Riccati difference equations provide an approach analogous to series solution methods for linear differential equations. The book develops several topics which have not been available at this level. In particular, the material of the chapters on continued fractions (Chapter 2), symplectic systems (Chapter 3), and discrete variational theory (Chapter 4) summarize recent literature. Similarly, the material on transforming Riccati equations presented in Chapter 3 gives a self-contained unification of various forms of Riccati equations. Motivation for our approach to difference equations came from the work of Harris, Vaughan, Hartman, Reid, Patula, Hooker, Erbe & Van, and Bohner.

Keywords

Matrix Matrix Theory Microsoft Access Optimal control boundary element method chemistry continued fraction difference equation form functions hamiltonian system presentation theorem variable variational problem

Authors and affiliations

  • Calvin D. Ahlbrandt
    • 1
  • Allan C. Peterson
    • 2
  1. 1.University of MissouriUSA
  2. 2.University of NebraskaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2467-7
  • Copyright Information Springer-Verlag US 1996
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4763-5
  • Online ISBN 978-1-4757-2467-7
  • Series Print ISSN 0927-4529
  • Buy this book on publisher's site