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For #1 I did not mean the zero-crossing of any one point, I meant the zero-crossings of the sum of all the derivatives of the kernel density function. Of course, whether it's efficient to calculate those zeros or not all depends on what the kernel density function is (probably not practical for gaussian, trivial for triangular, as two extereme cases)

Hmm... tricube sounds like an interesting one, though that's quite a bit of multiplication it uses. I wonder if this is the sort of thing that would be worth doing a rough approximation of really. I mean... it probably wouldn't affect the results too much to do the kernel density as a piecewise "sum of rectangles" approximation, and it would be much faster.