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Computable Analysis

An Introduction

  • Klaus Weihrauch

Table of contents

  1. Front Matter
    Pages I-X
  2. Klaus Weihrauch
    Pages 1-12
  3. Klaus Weihrauch
    Pages 13-49
  4. Klaus Weihrauch
    Pages 51-84
  5. Klaus Weihrauch
    Pages 85-122
  6. Klaus Weihrauch
    Pages 153-194
  7. Klaus Weihrauch
    Pages 195-235
  8. Klaus Weihrauch
    Pages 237-248
  9. Klaus Weihrauch
    Pages 249-268
  10. Back Matter
    Pages 269-285

About this book

Introduction

Is the exponential function computable? Are union and intersection of closed subsets of the real plane computable? Are differentiation and integration computable operators? Is zero finding for complex polynomials computable? Is the Mandelbrot set decidable? And in case of computability, what is the computational complexity? Computable analysis supplies exact definitions for these and many other similar questions and tries to solve them. - Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid basis for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.

Keywords

analysis complexity complexity in analysis computability computability in analysis computable analysis computable real functions computer computer science

Authors and affiliations

  • Klaus Weihrauch
    • 1
  1. 1.Fachbereich Informatik Theoretische Informatik IFern Universität HagenHagenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-56999-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66817-6
  • Online ISBN 978-3-642-56999-9
  • Series Print ISSN 1862-4499
  • Buy this book on publisher's site