高阶逼近Grünwald-Letnikov分数阶加权系数的快速算法

Fast algorithms for fractional Grünwald-Letnikov weighting coefficients with high-order approximation

文中提出三种求解高阶逼近任意运算阶的Grünwald-Letnikov分数阶微分器系数的快速算法,表述了算法的实现原理及对应的推导公式,并对其进行运行时间统计和计算复杂度分析。与幂级数展开法、卷积计算法、复化Simpson数值逼近法和IFFT相比,快速算法可以在误差允许的范围内,降低求解Grünwald-Letnikov分数阶微分器系数的计算复杂度,从而提高执行效率。

Three fast algorithms for Grünwald-Letnikov fractional digital differentiator coefficients with high-order approximations are proposed in this paper.The realization principles,corresponding derivation formulas,time statistics and computational-complexity analyzation of each algorithms are expressed.Compared with power series expansion method,the convolution algorithm,the complex Simpson integral and IFFT,new algorithms have the characteristics of easier computation and higher efficient within error tolerance.