Quaternionic step derivative: machine precision differentiation of holomorphic functions using complex quaternions

DOI10.1016/j.cam.2021.113699zbMath1472.65035arXiv2010.09543OpenAlexW3175763997WikidataQ117717426 ScholiaQ117717426MaRDI QIDQ2043200

Martin Roelfs, Daan Huybrechs, David Dudal

Publication date: 29 July 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.09543

zbMATH Keywords

automatic differentiationClifford algebrageometric algebracomplex analysiscomplex quaternionscomplex step derivative

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical differentiation (65D25)

Related Items (1)

Locating the closest singularity in a polynomial homotopy

Uses Software

• SymPy
• SciPy
• Python
• mftoolbox
• Algorithm 1008

Cites Work

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• Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals
• The complex step approximation to the Fréchet derivative of a matrix function
• Extensions of the first and second complex-step derivative approximations
• Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices
• Irreducible unitary representations of the Lorentz group
• Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
• Using Complex Variables to Estimate Derivatives of Real Functions
• Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition
• Algorithm 1008
• Space-Time Algebra
• Functions of Matrices
• The complex-step derivative approximation
• Numerical Differentiation of Analytic Functions

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