论文标题
Quaternionic步骤衍生物：使用复杂的四元组的机器精度分化
Quaternionic Step Derivative: Machine Precision Differentiation of Holomorphic Functions using Complex Quaternions
论文作者
论文摘要
已知的复杂步骤衍生物（CSD）方法可以通过评估实际数字线旁边的小虚构步骤来轻松准确地与实际分析函数的机器精度。当前的论文提出，可以通过沿Quaternionic方向迈出一小步来以类似的方式计算尸体函数的衍生物。已经证明，在这样做的CSD特性中，高精度和收敛性被传递到全态函数的衍生物中。为了证明实现的易度性，使用复杂的四元素，空间的几何代数和$ 2 \ times 2 $矩阵表示形式进行了数值实验。
The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them a small imaginary step next to the real number line. The current paper proposes that derivatives of holomorphic functions can be calculated in a similar fashion by taking a small step in a quaternionic direction instead. It is demonstrated that in so doing the CSD properties of high accuracy and convergence are carried over to derivatives of holomorphic functions. To demonstrate the ease of implementation, numerical experiments were performed using complex quaternions, the geometric algebra of space, and a $2 \times 2$ matrix representation thereof.
