Multicomplex Taylor Series Expansion for Computing High-Order Derivatives

dc.contributor.authorMillwater, Harry
dc.contributor.authorShirinkam, Sara
dc.creator.orcidhttps://orcid.org/0000-0001-7097-9283en_US
dc.date.accessioned2023-05-24T16:22:02Z
dc.date.available2023-05-24T16:22:02Z
dc.date.issued2014
dc.description.abstractMulticomplex 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<sup>th</sup> 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.departmentMechanical Engineeringen_US
dc.description.departmentMathematics
dc.description.sponsorshipNational Science Foundation; Air Force Office of Scientific Researchen_US
dc.identifier.citationMillwater, 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.v27i4.2en_US
dc.identifier.issn1314-8060
dc.identifier.otherhttp://dx.doi.org/10.12732/ijam.v27i4.2
dc.identifier.urihttps://hdl.handle.net/20.500.12588/1855
dc.language.isoen_USen_US
dc.publisherAcademic Publicationsen_US
dc.subjectcomplex Taylor series expansionen_US
dc.subjecthigh-order derivativesen_US
dc.subjectmulticomplex numbersen_US
dc.titleMulticomplex Taylor Series Expansion for Computing High-Order Derivativesen_US
dc.typeArticleen_US

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