Computer Aided Proofs in Analysis

Overview

This volume is the proceedings of a scientific conference on the use of computers to do exact mathematics which was held at the University of Cincinnati, March 22-25, 1989. One group of papers deals with the use of general algebraic processors like Macsyma, Reduce, Scratchpad etc. to do precise computations in bifurcation analysis and related areas of analysis. Another group of papers deals with the development of the software to solve equations exactly, carry of explicit integrations etc. for these general ...
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Paperback (Softcover reprint of the original 1st ed. 1991)
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Overview

This volume is the proceedings of a scientific conference on the use of computers to do exact mathematics which was held at the University of Cincinnati, March 22-25, 1989. One group of papers deals with the use of general algebraic processors like Macsyma, Reduce, Scratchpad etc. to do precise computations in bifurcation analysis and related areas of analysis. Another group of papers deals with the development of the software to solve equations exactly, carry of explicit integrations etc. for these general software packages. A third group discusses the use of interval arithmetic algorithms and software to give rigorous proofs of mathematical theorems and give precise estimates of stabililty regions.
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Editorial Reviews

Booknews
Contains some 20 papers from an April 1989 conference at the U. of Cincinnati. Aspects of using computer methods to obtain precise answers to questions in analysis are addressed by developers and end users in symbolic algebra, interval arithmetic, and other fields. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781461390947
  • Publisher: Springer New York
  • Publication date: 7/31/2012
  • Series: IMA Volumes in Mathematics and its Applications Series , #28
  • Edition description: Softcover reprint of the original 1st ed. 1991
  • Edition number: 1
  • Pages: 251
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.57 (d)

Table of Contents

The conversion of a high order programming language from floating-point arithmetic to range arithmetic.- Sylvester’s form of the resultant and the matrix-triangularization subresultant PRS method.- Computing the Tsirelson space norm.- Floating-point systems for theorem proving.- Computer algebra and indefinite integrals.- A computer-assisted approach to small-divisors problems arising in Hamiltonian mechanics.- On a computer algebra aided proof in bifurcation theory.- MACSYMA program to implement averaging using elliptic functions.- Validated anti-derivatives.- A toolbox for nonlinear dynamics.- Computer assisted proofs of stability of matter.- Accurate strategies for K.A.M. bounds and their implementation.- A software tool for analysis in function spaces.- Equation solving by symbolic computation.- Deciding a class of Euclidean geometry theorems with Buchberger’s algorithm.- Lie transform tutorial — II.- Interval tools for computer aided proofs in analysis.- Tools for mathematical computation.- Shadowing trajectories of dynamical systems.- Transformation to versal normal form.- Computer assisted lower bounds for atomic energies.
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