Art

J-GLOBAL ID：202002233765612896   Reference number：20A1990491

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

高次導関数を計算するための超双対数の行列表現の基本定理

Author (6)： Imoto Yusuke (Institute for Advanced Study, Kyoto University) ,  Yamanaka Naoya (School of Information Science, Meisei University) ,  Uramoto Takeo (Institute for Advanced Study, Kyoto University) ,  Tanaka Masato (Toyota Central R&D Laboratories, INC.) ,  Fujikawa Masaki (Faculty of Engineering Department of Mechanical Systems Engineering, University of the Ryukyus) ,  Mitsume Naoto (Faculty of Engineering, Information and Systems, University of Tsukuba)
Material： JSIAM Letters (Web)  (JSIAM Lett (Web))
Volume： 12  Page： 29-32(J-STAGE)  Publication year： 2020 
JST Material Number： U0115A  ISSN： 1883-0617  Document type： Article
Article type： 原著論文  Country of issue： Japan (JPN)  Language： ENGLISH (EN)

Thesaurus term： *number (mathematics) ,  *derivative ,  higher dimension ,  *numerical calculation ,  matrix (mathematics) ,  potential ,  Discriminant Analysis ,  numerical analysis ,  performance evaluation ,  characterization
Semi thesaurus term： *ハイパーデュアル数 ,  高次導関数 ,  characterization

Author keywords (5)： hyper-dual numbers ,  matrix representation ,  higher-order derivatives ,  HDN-M differentiation ,  automatic differentiation

JST classification (2)： System and control theory in general  (IA02010H) ,  Numerical computation  (JE02000J)

Reference (7)：

• 1) M. Ortiz and L. Stainier, The variational formulation of viscoplastic constitutive updates, Comput. Methods Appl. Mech. Engrg., 171 (1999), 419-444.
• 2) M. Tanaka, D. Balzani and J. Schroder, Implementation of incremental variational formulations based on the numerical calculation of derivatives using hyper dual numbers, Comput. Methods Appl. Mech. Engrg., 301 (2016), 216-241.
• 3) J. A. Fike, Multi-objective optimization using hyper-dual numbers, Ph.D. thesis, Stanford University, 2013.
• 4) W. K. Clifford, Preliminary sketch of biquaternions, Proc. Lond. Math. Soc., 4 (1873), 381-395.
• 5) E. Pennestri and R. Stefanelli, Linear algebra and numerical algorithms using dual numbers, Multibody Syst. Dyn., 18 (2007), 323-344.

Terms in the title (5)： 導関数 ,  計算 ,  行列 ,  表現 ,  定理