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 representation 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 an 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有力工具。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不封闭，且其使用会引入过度宽松的界限。另一方面，后来引入的多边形类型允许以更高计算成本实现上述运算的任意精确表示。我们提出多弧区间类型作为前述类型的有效扩展。多弧区间可精确表示所有原始区间及其大部分算术组合，并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，它能在比多边形类型更低计算成本下实现完美精度，这一点我们通过相关案例研究予以展示。本文对全部五种区间类型的算术性质进行了严谨分析，其中包含一种新的代数几何边界分析方法。