Conference Proceedings

Third International Conference on Advances in Computing, Electronics and Communication - ACEC 2015

Higher Order Approximations for Derivatives using Hypercomplex-Steps

Author(s) : H. M. NASIR

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.

Conference Title : Third International Conference on Advances in Computing, Electronics and Communication - ACEC 2015
Conference Date(s) : 10-11 October, 2015
Place : Hotel Novotel Zurich City-West, Zurich, Switzerland
No fo Author(s) : 1
DOI : 10.15224/978-1-63248-064-4-106
Page(s) : 193 - 198
Electronic ISBN : 978-1-63248-064-4
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