Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular (together called primitive) interval types are not closed under simple arithmetic operations and their use yields overly relaxed bounds. The later introduced polygonal type, on the other hand, allows for arbitrarily precise representaion of the above operations for a higher computational cost. We propose the polyarcular interval type as an effective extension of the previous types. The polyarcular interval can represent all primitive intervals and most of their arithmetic combinations precisely and has a approximation capability competing with that of the polygonal interval. In particular, in antenna tolerance analysis it can achieve perfect accuracy for lower computational cost then the polygonal type, which we show in a relevant case study. In this paper, we present a rigorous analysis of the arithmetic properties of all five interval types, involving a new algebro-geometric method of boundary analysis.

翻译：复区间算术是分析计算误差的强大工具。自然产生的矩形、极坐标和圆形（统称为原始）区间类型在简单算术运算下并非封闭的，并且其使用会产生过度宽松的界限。而后来引入的多边形类型允许以更高的计算成本对上述运算进行任意精确的表示。我们提出多弧区间类型作为先前类型的有效扩展。多弧区间可以精确表示所有原始区间及其大多数算术组合，并且具有与多边形区间相媲美的逼近能力。特别是在天线容差分析中，与多边形类型相比，它能够以更低的计算成本实现完美的精度，我们在相关的案例研究中展示了这一点。在本文中，我们对所有五种区间类型的算术性质进行了严格分析，涉及一种新的边界分析的代数几何方法。