## Kempten Autumn Talks

**Title of the lecture**

“Interval and affine computation”

**Lecturer**

Prof. Dr. Iwona Skalna

AGH Kraków

Kraków, Poland

**Time of the lecture**

December 03, 2020, 15:45 o’clock ETC

**Duration**

90 minutes (including discussion)

**Abstract**

Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to bound rounding errors and measurement errors in mathematical and numerical computation. Methods based on interval arithmetic can produce reliable results, i.e., results that are guaranteed to include the (unknown) exact result. Interval arithmetic has however a deficiency called the “dependency problem”. This deficiency can be partially eliminated by using affine forms which preserve first order dependency between input variables. Thanks to the use of affine forms the results are still (assuming proper implementation) reliable whereas the results are usually much tighter than the results of the same computation with interval arithmetic. Interval and affine computation are used to solve practical problems in the field of structural mechanics, electrical engineering, physics, and in game theory.