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Twins and f Algorithm

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2091)

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.

Keywords

  • Outer Approximation
  • Modal Intervals
  • Classical Intervals
  • Proper Twin
  • Improper Component

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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)

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  2. 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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