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Computers can work only with computable numbers, while most of the algorithms are based on analysis of real numbers (real analysis).

When I heard of the existence of computable analysis I immediately had these questions:

  • Can it help numerical analysis in some way?
  • Can we for example, help prove convergence of algorithms that are not convergent in the reals?
  • Can we find different algorithms that work for computables faster than they do for reals?
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    $\begingroup$ I'm not sure if it's strictly relevant to your question, but you might want to consider interval arithmetic too. Although I guess that's really attacking a similar problem from an engineering viewpoint. $\endgroup$ – origimbo Mar 1 '16 at 1:22
  • $\begingroup$ Yes, interval arithmetic is useful but conceptually it's not hard. Computable analysis seems to try to reinvent all of algebra for computers. $\endgroup$ – Milind R Mar 1 '16 at 1:43

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