We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several research communities for decades, but many mysteries remain. We present several open problems which we hope will be of broad interest.

翻译：我们综述了在精确算术（变精度）和有限算术（浮点）模型下，对复方阵进行近似对角化的高效算法方面的最新进展。尽管这一问题已在多个研究领域中被研究数十年，但仍有许多未解之谜。我们提出几个开放性问题，期望能引起广泛兴趣。