Multicomplex Taylor Series Expansion for Computing High-Order Derivatives
dc.contributor.author | Millwater, Harry | |
dc.contributor.author | Shirinkam, Sara | |
dc.creator.orcid | https://orcid.org/0000-0001-7097-9283 | en_US |
dc.date.accessioned | 2023-05-24T16:22:02Z | |
dc.date.available | 2023-05-24T16:22:02Z | |
dc.date.issued | 2014 | |
dc.description.abstract | Multicomplex Taylor series expansion (MCTSE) is a numerical method for calculating higher-order partial derivatives of a multivariable real-valued and complex-valued analytic function based on Taylor series expansion without subtraction cancelation errors. The implementation has been facilitated using Cauchy-Riemann matrix representation of multicomplex variables. In this paper, we show steps for finding these matrices and, in addition, that the number of appearances of the k-th derivatives follows the Pascal's triangle. Also, the situations where the MCTSE is not applicable is determined. Finally, we investigate the application of the method for complex-valued functions. | en_US |
dc.description.department | Mechanical Engineering | en_US |
dc.description.department | Mathematics | |
dc.description.sponsorship | National Science Foundation; Air Force Office of Scientific Research | en_US |
dc.identifier.citation | Millwater, H., & Shirinkam, S. (2014). Multicomplex Taylor Series Expansion for Computing High-Order Derivatives. International Journal of Applied Mathematics, 27(4), 311-334. doi:http://dx.doi.org/10.12732/ijam.v27i4.2 | en_US |
dc.identifier.issn | 1314-8060 | |
dc.identifier.other | http://dx.doi.org/10.12732/ijam.v27i4.2 | |
dc.identifier.uri | https://hdl.handle.net/20.500.12588/1855 | |
dc.language.iso | en_US | en_US |
dc.publisher | Academic Publications | en_US |
dc.subject | complex Taylor series expansion | en_US |
dc.subject | high-order derivatives | en_US |
dc.subject | multicomplex numbers | en_US |
dc.title | Multicomplex Taylor Series Expansion for Computing High-Order Derivatives | en_US |
dc.type | Article | en_US |
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