Occasionally, I attend seminars re applied math, typically discussing filters, or image processing, often involving high dimensional spaces.
The focus is usually the efficiency of the algorithms, or their accuracy, e.g. voice recognition. Of course they also try to prove theoretical correctness.
And there's the problem, in my view. They throw around gradients and conjugate gradients and Laplacians cavalierly. Which is perfectly valid theoretically, but numerically, doesn't this raise concerns? Isn't there a vast literature on the numerical difficulties in implementation? Especially for derivatives. But they say "no sweat, it's one line in MATLAB!" ??
Is my skepticism justified, or am I beating a dead horse? Granted that I'm not a real expert in the fine points -