A Polar Representation for Complex Interval Numbers

Authors

  • Arão Lyra UnP
  • Adrião Duarte Dória Neto UFRN
  • Benjamın René Callejas Bedregal UFRN
  • Roque Mendes Prado Trindade uesb

DOI:

https://doi.org/10.22481/recic.v1i1.4929

Keywords:

Complex Interval, Complex Interval Numbers, Complex Interval Variable

Abstract

The present work defines the basic elements for the introduction to the Study of Complex variables under the mathematical interval context with the goal of using it as a foundation for the understanding of pure mathematical problems, associating the mathematical interval to support the results. The present article contributes to the complex interval theory taking into consideration Euler’s Identity and redefining the polar representation of interval complex numbers. In engineering, the present article could be used as a subsidy for many applications where complex variable theory is applicable and requires accurate results.

Downloads

Download data is not yet available.

References

Acioly BM. Fundamentação computacional da matemática intervalar [tese]. Porto Alegre: Instituto de Informática, Universidade Federal do Rio Grande do Sul; 1991.

Arndt HR. On interval systems $[x] = [a][x] + [b]$ and the powers of interval matrices in complex interval arithmetics. Reliable Comput. 2007; 13: 245–259.

Blomquist F, Hofschuster W, Krämer W, Neher M. Complex interval functions in c-xsc. Preprint 2005/2 - Wissenschaftliches Rechnen/Softwaretechnologie; 2005.

Boche R. Complex interval arithmetic with some applications. Sunnyvale: Lockheed Missiles & Space Company; 1966. p. 1–33.

Candau Y, Raissi T, Ramdani N, Ibos L. Complex interval arithmetic using polar form. Reliable Comput. 2006; 12(1): 1–20.

Gonzales R, Wintz P. Digital Image Processing. 2. ed. [S.l.]: Addison and Wesley; 1987.

Irwin JD. Basic Engineering Circuit Analysis. 3. ed. [S.l.]: Macmillan Publishing; 1992.

Jaulin L. Path planning using intervals and graphs. Reliable Comput. 2001; 7: 1–15.

Kieffer M, Jaulin L, Walter É. Robust autonomous robot localization using interval analysis. Reliable Comput. 2000; 6(6): 337–362.

Kulisch UK, Miranker WL. Computer Arithmetic: Theory and Practice. [S.l.]: Academic Press; 1981.

Leveque O, Jaulin L, Meizel D, Walter É. Vehicle localization from inaccurate telemetric data: a set inversion approach. In: 5th IFAC Symposium on Robot Control (SY.RO.CO.’97); 1997.

Mascarenhas NDA, Velasco FRD. Processamento Digital de Imagens. In: IV Escola de Computação. 1985; 1: 235.

Moore RE. Interval analysis. New Jersey: Prentice Hall; 1966.

Moore RE. Methods and applications of interval analysis. Philadelphia: SIAM; 1979.

Moore RE. Computational functional analysis. Chichester: Ellis Horwood; 1985.

Oliveira PW, Diverio TA, Claudio DM. Fundamentos da matemática intervalar. Porto Alegre: Sagra Luzzatto; 1997.

Rocha LM, Kreinovich V. Computing Uncertainty in Interval Based Sets. In: Applications of Interval Computations. [S.l.]: Kluwer Academic; 1996.

Santana FT. Uma fundamentação para sinais e sistemas intervalares [tese]. Natal: Universidade Federal do Rio Grande do Norte; 2011.

Scott D. Outline of a Mathematical Theory of Computation [dissertação]. Oxford: Oxford University Computing Laboratory; 1970.

Spiegel MR. Complex variables: resum of the theory. 1. ed. [S.l.]: McGraw-Hill; 1981.

Toussaint GT. Computational Morphology: A Computational Geometric Approach to the Analysis of Form. 6. ed. [S.l.]: Software Books; 2000.

Downloads

Published

2019-03-29

How to Cite

LYRA, Arão; DÓRIA NETO, Adrião Duarte; BEDREGAL, Benjamın René Callejas; TRINDADE, Roque Mendes Prado. A Polar Representation for Complex Interval Numbers. Journal of Computer Science, [S. l.], v. 1, n. 1, p. p. 1–10, 2019. DOI: 10.22481/recic.v1i1.4929. Disponível em: https://periodicos2.uesb.br/recic/article/view/4929. Acesso em: 30 may. 2026.