Journals Proceedings

International Journal of Advances in Computer Science and Its Applications

Higher Order Approximations for Derivatives using Hypercomplex-Steps

Author(s) : H. M. NASIR


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.

No fo Author(s) : 1
Page(s) : 52 - 57
Electronic ISSN : 2250 - 3765
Volume 6 : Issue 1
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