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From Reals to Integers: Rounding Functions and Rounding Rules

In: Proportional Representation

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  • Friedrich Pukelsheim

    (Universität Augsburg, Institut für Mathematik)

Abstract

A rounding function maps non-negative quantities into integers. Examples are the floor function, the ceiling function, the commercial rounding function, and the even-number rounding function. A rounding rule maps non-negative quantities more lavishly into subsets of integers. Every rounding function or rounding rule induces a sequence of jumppoints, called signposts, where they advance from one integer to the next. Rounding rules map a signpost into the two-element set consisting of its neighboring integers, while non-signposts are mapped to singletons. Prominent examples are the rules of downward rounding, of standard rounding, and of upward rounding. The one-parameter families of stationary signposts and of power-mean signposts are of particular interest.

Suggested Citation

  • Friedrich Pukelsheim, 2017. "From Reals to Integers: Rounding Functions and Rounding Rules," Springer Books, in: Proportional Representation, edition 2, chapter 0, pages 59-70, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-64707-4_3
    DOI: 10.1007/978-3-319-64707-4_3
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