Reliable computation

A method of computation that guarantees correctness of the result obtained. Any algorithm calculating a real number (or numbers) cannot be absolutely correctly implemented on a computer, due to the finite representation of real numbers in computers. Instead of obtaining a single value for the result, one obtains a set containing the desired value. In the simplest case one may consider the set to be an interval.

In this connection, a special role in reliable computation is played by interval analysis (or, more generally, interval mathematics). The interval approach allows one to obtain guaranteed estimates for unknown real values. Within the framework of reliable computation theory one considers not only applied aspects (i.e., methods for obtaining guaranteed estimates), but also abstract problems emerging from internal requirements of the theory.

Interval analysis is not the only field that is subsumed under the term "reliable computation" . The following branches of mathematics also belong here: symbolic computations that permit reformulation of the problem conditions and modification of its solution algorithm while preserving the set of results; the theory of convincing programming and program optimization; and problems of representing mathematical objects, above all arbitrary numbers and functions, by (mapping them onto) a finite set of representable objects. Other fields participating in the implementation of reliable computation belong to computer science, e.g., issues of computer architecture and the system of basic operators for calculations with guaranteed result. To carry out a reliable computation one has to use specialized software. To encode algorithms on a computer, special language means are required. These are also considered in the theory of reliable computation.