What question did this study set out to answer?

The aim is to enhance the accuracy and efficiency of approximating partial derivatives for functions with multiple variables.

Advances in High Precision Partial Derivative Approximation for Functions of n Variables

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Review extends complex step approach for accurate partial derivatives in vector functions, highlighting efficiency.

The aim is to enhance the accuracy and efficiency of approximating partial derivatives for functions with multiple variables.
Extended the complex step method for approximating partial derivatives.
Demonstrated the method's application in various programming languages like MATLAB, Python, and C++.
Provided illustrative examples, including applications in astrodynamics.
Achieved 15-digit precision for first partial derivatives using 64-bit arithmetic.
Obtained 10 to 13 digit precision for second partial derivatives.
Achieved 5 to 8 digit precision for third-order partial derivatives.

Yamamoto et al. (2026) studied this question.

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