A Possibility for Combining Ideas from the Interval Analysis
and the Constructive Mathematical Analysis
Dimiter Skordev
Abstract. The notion of interval computability of a function
is introduced and investigated. A continuous real-valued function, whose
domain is an open set of real numbers, is called interval computable
if, whenever a closed bounded interval is included in the domain of the
function and an algorithm is given for computing arbitrarily good rational
approximations of the end points of this interval, one can effectively
construct an algorithm for computing arbitrarily good rational approximations
of the minimal and the maximal value of the function in the interval. A
way is pointed out for applying one of the obtained results to the approximate
calculation of function values.