Exact real arithmetic

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Revision as of 11:25, 22 April 2006 by EndreyMark (talk | contribs) (or ,,computable reals'', a topic embracing analysis, arithmetic, computability. Introductory text, and links: 1) Vuillemin's strong theoretical foundation article 2) Exact Computation, a portal-like)

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Introduction

Exact real arithmetic is an interesting area: it is a deep connection between

  • numeric methods
  • and deep theoretic fondations of algorithms (and mathematics).

Its topic: computable real numbers raise a lot of interesting questions rooted in mathematical analysis, arithmetic, but also computability theory (see numbers-as-programs approaches).

Computable reals can be achieved by many approaches -- it is not one single theory.

Theory

Jean Vuillemin's Exact real computer arithmetic with continued fractions is very good article on the topic itself. It can serve also as a good introductory article, too, because it presents the connections to both mathematical analysis and computability theory. It discusses several methods, and it describes some of them in more details.

Portal-like homepages

Exact Computation

There are functional programming materials too, even with downloadable Haskell source.