Improved Arithmetic of Complex Fans

SOYLU G.

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, vol.47, no.2, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1145/3434400
  • Journal Name: ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, DIALNET, Civil Engineering Abstracts
  • Keywords: Interval arithmetic, complex sets, polar form
  • Akdeniz University Affiliated: Yes

Abstract

Complex fans are sets of complex numbers whose magnitudes and angles range in closed intervals. The fact that the sum of two fans is a disordered shape gives rise to the need for computational methods to find the minimal enclosing fan. Cases where the sum of two fans contains the origin of the complex plane as a boundary point are of special interest. The result of the addition is then enclosed by circles in current methods, but under certain circumstances this turns out to be an overestimate. The focus of this article is the diagnosis and treatment of such cases.