# Are there any benefits of computable analysis to numerical algorithms

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?
• 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. – origimbo Mar 1 '16 at 1:22
• Yes, interval arithmetic is useful but conceptually it's not hard. Computable analysis seems to try to reinvent all of algebra for computers. – Milind R Mar 1 '16 at 1:43