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Dergiler / Gazi University Journal of Science / 2026 / Volume: 35 Issue: 1

On Complex Interval Arithmetic Using Polar Form

Edrees Mahmood(University of Mosul)0000-0002-4927-573X
Gültekin Soylu(AKDENIZ UNIVERSITY)0000-0003-2640-5690
Sayfa
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Yayın Tarihi
2022-03-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is also shown by examples that the proposed algorithms perform much better than their ancestors and avoid their errors.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, complex arithmetic in polar form, briefly sectors arithmetic is discussed.
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Temel Bulgular & Veri:The algorithms are implemented in MATLAB R2020a and tested for all cases.
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Sonuç & Katkı:It is also shown by examples that the proposed algorithms perform much better than their ancestors and avoid their errors.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Interval arithmetic · Complex sets · Polar form

Abstract

In this paper, complex arithmetic in polar form, briefly sectors arithmetic is discussed. The fact that the family of sectors is not closed under addition and subtraction gives rise to the need of an optimized approximation. Precisely, the problem discussed, is to determine the smallest possible sector that contains the sum of two sectors. An efficient algorithm that is solving this problem is introduced and compared with existing algorithms in the literature. The algorithms are implemented in MATLAB R2020a and tested for all cases. It is also shown by examples that the proposed algorithms perform much better than their ancestors and avoid their errors.

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Bu Makaleye Atıf Yap

Mahmood, E., Soylu, G. (2022). On Complex Interval Arithmetic Using Polar Form. Gazi University Journal of Science, Volume: 35 Issue: 1. https://doi.org/10.35378/gujs.833690

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Kaynakça (7)

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  2. Mahmood, E. M.N. and Soylu, G., “An effective method for division of rectangular intervals”, AIMS Mathematics, 5(6): 6355–6372, (2020). DOI: 10.3934/math.2020409
  3. Boche, R., “Complex Interval Arithmetic with Some Applications”, Lockheed Missiles and Space Company, 4-22-66-1, Sunnyvale, California, (1966).
  4. Henri, P., “Circular arithmetic and the determination of polynomial zeros”, Springer Lecture Notes, 228: 86-92, (1971).
  5. Klatte, R. and Ulrich, K., “Complex sector arithmetic”, Computing, 24(2): 139–148, (1980).
  6. Flores, J., “Complex Fans: A Representation for vectors in polar form with interval attributes”, ACM Transactions on Mathematical Software, 25(2): 129-156, (1999).
  7. Candau, Y., Raissi, T., Ramdani, N. and Ibos, L., “Complex interval arithmetic using polar form”, Reliable Computing, 12: 1-20, (2006).