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Distances, Norms and Error Propagation in Idempotent Semirings

  • Roland Glück
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11194)

Abstract

Error propagation and perturbation theory are well-investigated areas of mathematics dealing with the influence of errors and perturbations of input quantities on output quantities. However, these methods are restricted to quantities relying on real numbers under traditional addition and multiplication. We aim to present first steps of an analogous theory on idempotent semirings, so we define distances and norms on idempotent semirings and matrices over them. These concepts are used to derive inequalities characterizing the influence of changes in the input quantities on the output quantities of some often used semiring expressions.

Notes

Acknowledgments

The author is grateful to the anonymous referees for helpful and enlightening remarks, especially to the fourth reviewer for his deep reflections about doing and selling science.

Supplementary material

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Deutsches Zentrum für Luft- und RaumfahrtAugsburgGermany

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