- 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.