4 ms·
This is a standard technique in numerical analysis for complex-differentiable functions, it's just not so common to have inputs be guaranteed to be holomorphic
by conistonwater 7y ago
This is a standard technique in numerical analysis for complex-differentiable functions, it's just not so common to have inputs be guaranteed to be holomorphic so people don't use it often, http://mpmath.org/doc/current/calculus/differentiation.html#mpmath.diff http://mpmath.org/doc/current/calculus/differentiation.html#... (https://github.com/fredrik-johansson/mpmath/blob/981102736a843ae30c26f73b388fdba622a46270/mpmath/calculus/differentiation.py#L198 https://github.com/fredrik-johansson/mpmath/blob/981102736a8...)
- kkylin 7y agoIndeed a standard technique in numerical analysis. Among the advantages of doing things this way (when applicable, i.e., when one has holomorphic integrands) are significantly better accuracy & stability: https://people.maths.ox.ac.uk/trefethen/sirev56-3_385.pdf https://people.maths.ox.ac.uk/trefethen/sirev56-3_385.pdf (Haven't looked closely at the posted code so no idea how directly relevant this is.)