@article{mes-tou-06-aa-quadr,
  author = {Messine, F. and Touhami, A.},
  title = {A General Reliable Quadratic Form: {An} Extension of Affine Arithmetic},
  journal = {Reliable Computing},
  volum = {12},
  pages = {171--192},
  year = 2006,
  doi = {10.1007/s11155-006-7217-4},
  comment = {Degree 2 extension of AA. Use in optimization.}, 
  abstract = {In this article, a new extension of affine arithmetic is introduced. This technique is based on a quadratic form named general quadratic form. We focus here on the computation of reliable bounds of a function over a hypercube by using this new tool. Some properties of first quadratic functions and then polynomial ones are reported. In order to show the efficiency of such a method, ten polynomial global optimization problems are presented and solved by using an interval branch-and-bound based algorithm.}
}