# Time complexity of derivation, gradient,differential, jacobian matrix

what is the time complexity of gradient $$\nabla_{f}$$ using the $$\mathcal O$$-notation? what is the time complexity of jacobian matrix using the $$\mathcal O$$-notation? who knows some references to introduce the time complexity of gradient? I make reply to reviewers for computational complexity of gradient and matrix operations. I need some references to cite.

• For the numerical calculation of a 1D derivative at a single point, you require at least two points (left aside methods like the complex step-derivative). So that's O(1). You can carry that forward to higher dimensions and then to vectors and matrices. – davidhigh Oct 15 at 12:19
• What algorithms are you using to compute your derivatives? Finite differencing? Automatic Differentiation (in forward or reverse mode)? How complicated is $f$? – Brian Borchers Oct 16 at 1:48