In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis.
Computable real numbers
Computable real functions
The computable real numbers form a real closed field (Weihrauch 2000, p. 180). The equality relation on computable real numbers is not computable, but for unequal computable real numbers the order relation is computable.
Computable real functions map computable real numbers to computable real numbers. The composition of computable real functions is again computable. Every computable real function is continuous (Weihrauch 2000, p. 6).
- Oliver Aberth (1980), Computable analysis, McGraw-Hill, ISBN 0-0700-0079-4.
- Marian Pour-El and Ian Richards, Computability in Analysis and Physics, Springer-Verlag, 1989.
- Stephen G. Simpson (1999), Subsystems of second-order arithmetic.
- Klaus Weihrauch (2000), Computable analysis, Springer, ISBN 3-540-66817-9.