Computing

, Volume 33, Issue 1, pp 27–35

# On the k-th root in circular arithmetic

• Ljiljana Petković
• M. Petković
Contributed Papers

## Abstract

The representation of thek-th root of a complex circular intervalZ={c;r} is considered in this paper. Thek-th root is defined by the circular intervals which include the exact regionZ1/k={z:zk∈Z}. Two representations are given: (i) the centered inclusive disks$$\cup \{ c^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} ; \mathop {\max }\limits_{z \in Z} |z^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} - c^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} |\}$$ and (ii) the diametrical inclusive disks with the diameter which is equal to the diameter of the regionZ1/k.

30E99

## Key words

Computational complex analysis circular interval arithmetic

# Über die k-te Wurzel in der Kreisarithmetik

## Zusammenfassung

In diesem Artikel hat die Darstellung derk-ten Wurzel des komplexen KreisintervallsZ={c;r} übergelegt. Diek-te Wurzel wurde mit den Kreisintervallen definiert, welche das richtige GebietZ1/k={z:zk∈Z} einschließen. Zwei Darstellungen sind gegeben: (i) zentrierte inklusive Kreisscheiben$$\cup \{ c^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} ; \mathop {\max }\limits_{z \in Z} |z^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} - c^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} |\}$$ und (ii) diametrische inklusive Kreisscheiben mit Diameter wie Diameter des GebietsZ1/k.

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