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math.NA2026
Efficient Computation of Arbitrary-Order Directional Derivatives in Multiple Directions via Generalized Dual Numbers
F. Peñuñuri, K. B. Cantún-Avila, O. Carvente +1
Arbitrary-order directional derivatives along multiple (possibly distinct) directions are computed through a generalized dual-number formulation for both scalar- and vector-valued…
math.NA2025
Dual Numbers for Arbitrary Order Automatic Differentiation
F. Peñuñuri, K. B. Cantún-Avila, R. Peón-Escalante
Dual numbers are a well-established tool for computing derivatives and constitute the basis of forward-mode automatic differentiation. While the theoretical framework for computing…
math.NA2023
A dual number formulation to efficiently compute higher order directional derivatives
R. Peón-Escalante, K. B. Cantún-Avila, O. Carvente +2
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemente…