著者
Yusuke Imoto Naoya Yamanaka Takeo Uramoto Masato Tanaka Masaki Fujikawa Naoto Mitsume
出版者
The Japan Society for Industrial and Applied Mathematics
雑誌
JSIAM Letters (ISSN:18830609)
巻号頁・発行日
vol.12, pp.29-32, 2020 (Released:2020-06-01)
参考文献数
7
被引用文献数
4

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.

言及状況

外部データベース (DOI)

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論文が出版されました。高階微分や偏微分を含む、関数の積や合成関数の微分公式の演算手順が行列演算で表現できることをhyper-dual numbers(超双対数)という二乗して0となる仮想的な数を用いて示しました。 https://t.co/STI87vIhV8
@imosuke24 そのURL,自分の環境では飛べませんでしたが・・・.下では飛べました. https://t.co/dCAPDIyACV

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