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Computer Aided Proofs in Analysis

  • Book
  • © 1991

Overview

Editors:
  1. Kenneth R. Meyer

    1. Departments of Mathematics and Computer Science, University of Cincinnati, Cincinnati, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Dieter S. Schmidt

    1. Department of Computer Science, University of Cincinnati, Cincinnati, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 28)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. The Conversion of a High Order Programming Language from Floating-Point Arithmetic to Range Arithmetic

    • Oliver Aberth
    Pages 1-4

  3. Sylvester’s form of the Resultant and the Matrix-Triangularization Subresultant PRS Method

    • Alkiviadis G. Akritas
    Pages 5-11

  4. Computing the Tsirelson Space Norm

    • Johnnie W. Baker, Oberta A. Slotterbeck, Richard Aron
    Pages 12-21

  5. Floating-Point Systems for Theorem Proving

    • G. Bohlender, J. Wolff von Gudenberg, W. L. Miranker
    Pages 22-32

  6. Computer Algebra and Indefinite Integrals

    • Manuel Bronstein
    Pages 33-42

  7. A Computer-Assisted Approach to Small-Divisors Problems Arising in Hamiltonian Mechanics

    • Alessandra Celletti, Luigi Chierchia
    Pages 43-51

  8. On a Computer Algebra Aided Proof in Bifurcation Theory

    • Carmen Chicone, Marc Jacobs
    Pages 52-70

  9. MACSYMA Program to Implement Averaging Using Elliptic Functions

    • Vincent T. Coppola, Richard H. Rand
    Pages 71-89

  10. Validated Anti-Derivatives

    • George F. Corliss
    Pages 90-96

  11. A Toolbox for Nonlinear Dynamics

    • Shannon Coffey, André Deprit, Étienne Deprit, Liam Healy, Bruce R. Miller
    Pages 97-115

  12. Computer Assisted Proofs of Stability of Matter

    • R. de la Llave
    Pages 116-126

  13. Accurate Strategies for K.A.M. Bounds and Their Implementation

    • R. De La Llave, D. Rana
    Pages 127-146

  14. A Software Tool for Analysis in Function Spaces

    • J.-P. Eckmann, A. Malaspinas, S. Oliffson Kamphorst
    Pages 147-167

  15. Equation Solving by Symbolic Computation

    • Anthony C. Hearn
    Pages 168-174

  16. Deciding a Class of Euclidean Geometry Theorems with Buchberger’s Algorithm

    • Bernhard Kutzler
    Pages 175-189

  17. Lie Transform Tutorial — II

    • Kenneth R. Meyer
    Pages 190-210

  18. Interval Tools for Computer Aided Proofs in Analysis

    • Ramon E. Moore
    Pages 211-216

  19. Tools for Mathematical Computation

    • L. B. Rall
    Pages 217-228

  20. Shadowing Trajectories of Dynamical Systems

    • Tim Sauer, James A. Yorke
    Pages 229-234
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Keywords

About this book

This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989. Each year the 19 Participating Institutions select, through a competitive process, several conferences proposals from the PIs, for partial funding. This conference brought together leading figures in a number of fields who were interested in finding exact answers to problems in analysis through computer methods. We thank Kenneth Meyer and Dieter Schmidt for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the dawn of the computer revolution the vast majority of scientific compu­ tation has dealt with finding approximate solutions of equations. However, during this time there has been a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, number theory and combina­ torics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools.

Editors and Affiliations

  • Departments of Mathematics and Computer Science, University of Cincinnati, Cincinnati, USA

    Kenneth R. Meyer

  • Department of Computer Science, University of Cincinnati, Cincinnati, USA

    Dieter S. Schmidt

Bibliographic Information

  • Book Title: Computer Aided Proofs in Analysis

  • Editors: Kenneth R. Meyer, Dieter S. Schmidt

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4613-9092-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1991

  • Softcover ISBN: 978-1-4613-9094-7Published: 16 December 2011

  • eBook ISBN: 978-1-4613-9092-3Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: XVI, 251

  • Topics: Analysis

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