Higher Order Approximations for Derivatives using Hypercomplex-Steps
نویسنده
چکیده
Complex-step differentiation is a recent popular method to compute a real valued function and its first derivative approximately with second order error using imaginary step size. We propose a generalization of complex-step method to compute a complex valued function and its derivatives up to order n – 1 with approximate error of order n, for any desired integer n. For this, we use a hypercomplex number system of dimension n and Taylor series expansion of the function at a hypercomplex number. Computations can be performed efficiently by using fast Fourier transform. Keywords—complex-step differentiation, hypercomplex numbers, automatic differentiation, algorithmic differentiation
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