Affine Arithmetic

Since 2007 One of my main domain is the computation of bounds of non-convex function over an interval. The most famous one are interval arithmetic, the Taylor expansion and Baumann center form. I became interested in particular to affine arithmetic that I developed and improve performance by offering new operators and new computation way. The standard affine arithmetic is another approach to calculate lower bounds and upper bounds of explicit function over an interval. It was introduced in 1993 by Comba and Stolfi and developed by De Figueiredo and Stolfi. The idea is to build an inclusion function based on affine forms. The idea is to keep linear information during the computation. This reduce the generated error, due to repetation of variables.

Extensions developed by Messine allow to limit the size of the affine form and to control the generated error. On this principle, I developed new arithmetic combining interval arithmetic and affine arithmetic, with a reliable, robust and effective implementation.