Abstract
This chapter deals with the construction of an algorithm to obtain inner and outer approximations of the f ∗ extension of a continuous function f, in the case of non-monotony of f in the studied domain. One convenient approach, but not the only one, is to simultaneously work with both inner and outer approximations. This kind of interval representation, referred to as twins, have already been studied in the field of classical intervals [55, 64]. First of all, twins with modal intervals will be presented.
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References
V.M. Kreinovich, V. Nesterov, N.A. Zheludeva, Interval methods that are guaranteed to underestimate (and the resulting new justification of kaucher arithmetic). Reliable Comput. 2(2), 119–124 (1996)
V. Nesterov, Interval and twin arithmetics. Reliable Comput. 3(4), 369–380 (1997)
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Sainz, M.A., Armengol, J., Calm, R., Herrero, P., Jorba, L., Vehi, J. (2014). Twins and f ∗Algorithm. In: Modal Interval Analysis. Lecture Notes in Mathematics, vol 2091. Springer, Cham. https://doi.org/10.1007/978-3-319-01721-1_7
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DOI: https://doi.org/10.1007/978-3-319-01721-1_7
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-01721-1
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