@inbook{ska-18-aa-altern,
  author = {Iwona Skalna},
  title = {Alternative Arithmetic},
  bookTitle = {Parametric Interval Algebraic Systems},
  year = 2018,
  publisher = {Springer},
  pages = {25--50},
  chapter = {2},
  isbn = {978-3-319-75187-0},
  doi = {10.1007/978-3-319-75187-0_2},
  comment = {Surveys various alternative models such as ellipsoid calculus and various types of AA},
  abstract = {Over the years, a lot of effort has been put into the development of self-validated computational (SVC) models that will be able to overcome the ``memoryless nature'' of interval arithmetic, i.e., to take into account the dependencies between variables involved in a computation and/or reduce the so-called wrapping effect. This effort has resulted in several such models worth mentioning: ellipsoid calculus (Chernousko, Izv Akad Nauk SSSR, Tekh Kibern 3:3--11; 4:3--11; 5:5--11, 1980, [27]), V{\'a}lyi, Ellipsoidal calculus for estimation and control, Birkh{\"a}user, Boston, 1997, [269]), constrained interval arithmetic (Lodwick, Constrained interval arithmetic, 1999, [131]), Hansen's generalized interval arithmetic (Hansen, A generalized interval arithmetic, Springer, Berlin, 1975, [72]), affine arithmetic (de Figueiredo, Stolfi, Self-validated numerical methods and applications, 1997, [33]), reduced affine arithmetic (Messine, New affine forms in interval branch and bound algorithms, 1999, [139]), and revised affine arithmetic (Vu, Sam-Haroud, Faltings, A generic scheme for combining multiple inclusion representations in numerical constraint propagation, 2004, [271]).}
}