Higher Order Approximations for Derivatives using Hypercomplex-Steps

H. M., NASIR (2015) Higher Order Approximations for Derivatives using Hypercomplex-Steps. In: Third International Conference on Advances in Computing, Electronics and Communication - ACEC 2015, 10-11 October, 2015, Zurich, Switzerland.

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Abstract

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.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: complex-step differentiation, hypercomplex numbers, automatic differentiation, algorithmic differentiation
Depositing User: Mr. John Steve
Date Deposited: 20 Apr 2019 11:36
Last Modified: 20 Apr 2019 11:36
URI: http://publications.theired.org/id/eprint/1422

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