|Title of host publication||The Princeton Companion to Applied Mathematics|
|Editors||Nicholas J Higham, Mark R Dennis, Paul Glendinning, Paul A Martin, Fadil Santosa, Jared Tanner|
|Place of Publication||Princeton NJ USA|
|Publisher||Princeton University Press|
|Number of pages||2|
|Publication status||Published - 2015|
Interval analysis is a calculus based on set-valued mathematics.In its simplest (and by far most popular) form, it builds upon interval arithmetic, which is a natural extension of real-valued arithmetic. Despite its simplicity, this kind of set-valued mathematics has a very wide range of applications in computer-aided proofs for continuous problems. In a nutshell, interval arithmetic enables us to bound the range of a continuous function, i.e., it produces a set enclosing the range of a given function over a given domain. This, in turn, enables us to prove mathematical statements that use open conditions, such as strict inequalities, fixed-point theorems, etc.