Alternative Arithmetic

Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 766)

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]), Vályi, Ellipsoidal calculus for estimation and control, Birkhäuser, 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]).

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Applied Computer Science, Faculty of ManagementAGH University of Science and TechnologyKrakówPoland

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