Fundamental theorem of matrix representations of hyper-dual numbers for computing higher-order derivatives

被引：0

作者：

Imoto, Yusuke ^{[1
]}

Yamanaka, Naoya ^{[2
]}

Uramoto, Takeo ^{[1
]}

Tanaka, Masato ^{[3
]}

Fujikawa, Masaki ^{[4
]}

Mitsume, Naoto ^{[5
]}

机构：

[1] Kyoto Univ, Inst Adv Study, Sakyo Ku, Yoshida Ushinomiya Cho, Kyoto 6068501, Japan

[2] Meisei Univ, Sch Informat Sci, 2-1-1 Hodokubo, Hino, Tokyo 1918506, Japan

[3] Toyota Cent Res & Dev Labs Inc, 41-1 Yokomichi, Nagakute, Aichi 4801192, Japan

[4] Univ Ryukyus, Dept Mech Syst Engn, Fac Engn, 1 Senbaru, Nishihara, Okinawa 9030213, Japan

[5] Univ Tsukuba, Fac Engn Informat & Syst, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058577, Japan

来源：

JSIAM LETTERS | 2020年 / 12卷

关键词：

hyper-dual numbers; matrix representation; higher-order derivatives; HDN-M differentiation; automatic differentiation;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：29 / 32

页数：4

共 7 条

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