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

DOI10.14495/jsiaml.12.29OpenAlexW3029488698MaRDI QIDQ5121397

Naoya Yamanaka, Masaki Fujikawa, Takeo Uramoto, Masato Tanaka, Naoto Mitsume, Yusuke Imoto

Publication date: 14 September 2020

Published in: JSIAM Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.14495/jsiaml.12.29

zbMATH Keywords

automatic differentiationmatrix representationhigher-order derivativeshyper-dual numbers

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Numerical differentiation (65D25)

Related Items (2)

The Application of Euler-Rodrigues Formula over Hyper-Dual Matrices ⋮ Hyper-dual number-based numerical differentiation of eigensystems

Cites Work

• A highly accurate 1st- and 2nd-order differentiation scheme for hyperelastic material models based on hyper-dual numbers
• The variational formulation of viscoplastic constitutive updates
• Implementation of incremental variational formulations based on the numerical calculation of derivatives using hyper dual numbers
• Linear algebra and numerical algorithms using dual numbers

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