We show, that the Complex Step approximation to the Fr\'echet derivative of real matrix functions is applicable to the matrix sign, square root and polar mapping using iterative schemes. While this property was already discovered for the matrix sign using Newton's method, we extend the research to the family of Pad\'e iterations, that allows us to introduce iterative schemes for finding function and derivative values while approximately preserving automorphism group structure.

翻译：我们显示,对于真实矩阵函数的Fr\'echet衍生物的复杂步骤近似值适用于使用迭接图案的矩阵符号、平根和极地绘图。 虽然已经发现了该属性,用于使用牛顿方法的矩阵符号,但我们将研究扩展至Pad\'e迭代的家族,这使我们能够引入迭代计划,以查找函数和衍生值,同时大致保持自成形群的结构。