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Numerical Algorithms

Calculation of machine precision second order derivatives using dual-complex numbers

  • 04-10-2024
  • Research
Published in:
Authors
H. Millwater
M. Balcer
N. Millwater
Published in
Numerical Algorithms | Issue 4/2025

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Abstract

The article introduces a novel approach to calculating machine precision second order derivatives by leveraging dual-complex numbers. It begins by discussing the limitations of current methods using complex and dual numbers for first order derivatives. The authors then present the concept of dual-complex numbers, which combines the strengths of both complex and dual numbers, allowing for the accurate computation of second order derivatives. The methodology is detailed, including the equations and procedures for both univariate and multivariate functions. The paper also includes numerical examples and comparisons to demonstrate the effectiveness of the dual-complex method. Additionally, it provides practical guidelines for selecting step sizes and highlights the advantages of this approach over traditional methods and more complex alternatives like bicomplex and bidual numbers.
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previous article An adaptive finite point scheme for the two-dimensional coupled burgers’ equation
next article Multivariate polynomial interpolation based on Radon projections
Title
Calculation of machine precision second order derivatives using dual-complex numbers
Authors
H. Millwater
M. Balcer
N. Millwater
Publication date
04-10-2024
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2025
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-024-01937-2
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