On Complex Interval Arithmetic Using 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.

Keywords

• Interval arithmetic
• Complex sets
• Polar form
• Global optimization

References

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