## Section: New Results

### Interval Arithmetic

Participants : Vincent Lefèvre, Hong Diep Nguyen, Nathalie Revol.

#### Efficient Implementation of Algorithms for Interval Linear Algebra

H.-D. Nguyen and N. Revol [49] proposed an algorithm for interval linear system solving, based on iterative refinement techniques and on a relaxation of the interval linear system. This algorithm is competitive with the best competitors in terms of efficiency while obtaining more accurate solutions. Ongoing work is the development of an algorithm for interval matrix product: this algorithm is a tradeoff between speed – it is almost as fast as the implementation in IntLab – and accuracy – the overestimation is smaller.

#### Standardization of Interval Arithmetic

We contributed to the creation, and now chair, an IEEE working group on the standardization of interval arithmetic. The main achievements of this working group, for the year 2009, are a working framework (notations, structure in levels), the first basic definitions (interval, arithmetic operations, elementary functions) and finally implementation issues (exception handling). We envision future discussion to address other operations on intervals (endpoints, midpoint...), on sets (union, intersection...), comparison and we will do our best to impel work on these topics.