Numerical derivatives through finite-difference approximations can be calculated using the 'pnd' package with parallel capabilities and optimal step-size selection to improve accuracy. These functions facilitate efficient computation of derivatives, gradients, Jacobians, and Hessians, allowing for more evaluations to reduce the mathematical and machine errors. Designed for compatibility with the 'numDeriv' package, which has not received updates in several years, it introduces advanced features such as computing derivatives of arbitrary order, improving the accuracy of Hessian approximations by avoiding repeated differencing, and parallelising slow functions on Windows, Mac, and Linux.
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