@incollection{cha-rou-20-aa-affine,
  title = {Affine Arithmetic},
  author = {Chakraverty, Snehashish and Rout, Saudamini},
  booktitle = {Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems},
  series = {Synthesis Lectures on Mathematics {\&} Statistics},
  year = 2020,
  pages = {39-51},
  doi = {10.1007/978-3-031-02424-5_3},
  comment = {Overview of affine arithmetic.},
  abstract = {In 1993, Comba and Stolfi gave us the basic idea of affine arithmetic [Comba and Stolfi (1993) [3]]. The interval dependency problem that occurs in standard interval arithmetic is the main cause behind development of affine arithmetic. Affine arithmetic is a self-validated numerical model that records the range for each ideal quantity and also keeps track of first-order correlations between these quantities. For this additional information, the approximation error is incurred in each operation of affine arithmetic. Therefore, affine arithmetic can overcome the extreme increment of the width of the resulting interval. This benefit will help for several chained-interval computations where interval arithmetic goes through an error explosion. Also, affine arithmetic provides the geometric representation of joint ranges for the related quantities, which may be useful for different interval methods.}
}