JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
Articles
Fundamental theorem of matrix representations of hyper-dual numbers for computing higher-order derivatives
Yusuke ImotoNaoya YamanakaTakeo UramotoMasato TanakaMasaki FujikawaNaoto Mitsume
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2020 Volume 12 Pages 29-32

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Abstract

Hyper-dual numbers (HDN) are numbers defined by using nilpotent elements that differ from each other. The introduction of an operator to extend the domain of functions to HDN space based on Taylor expansion allows higher-order derivatives to be obtained from the coefficients. This study inductively defines matrix representations of HDN and proposes a numerical method for higher-order derivatives, called HDN-M differentiation, based on the matrix representations of HDN. The proposed method is characterized so that higher-order derivatives can be computed with matrix operation rules without implementations of the operation rules of HDN.

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© 2015, The Japan Society for Industrial and Applied Mathematics
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