CHAPTER 14Multiple Differentiation in Almost Constant Time

14.1 MULTIDIMENSIONAL DIFFERENTIATION

In this chapter, we discuss the efficient differentiation of multidimensional functions. In general terms, we have a function:

images

that produces images results images out of images inputs images. The function images is implemented in code and we want to compute its images Jacobian matrix:

images

as efficiently as possible.

We have seen that AAD run time is constant in images, but linear in images, and that this is the case even when the evaluation of is constant ...

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