Talk:Sparse grid

This page badly needs examples: First, illustrations of sparse grids in 2D (showing different levels of descretization), and second, steps in constructing one of the sparse grids. Without the latter, the formula is too hard to interpret. I guess $$Q_l^{(d)}$$ is a set of $$2^l$$ points, each of dimension $$d$$, and $$-$$ represents set difference. However, the operation $$\otimes$$ needs explanation.

Could the statement "A $$1-d$$ integration on level $$i$$ is computed by the evaluation of $$O(2^{i})$$ points" be restated as "A one-dimensional integration..."? If so, it should be. Note that $$d$$ is a variable already being used, so $$1-d$$ is a (nonpositive) number. However, a phrase like "-2 integration" does not make sense. Jrvz 11:48, 16 August 2007 (UTC)

Bad notation & Should be under numerical integration.
I understand the desire to match form and function, using l when you're also using i is just bad typography, especially with the number of mobile devices with smaller screens being developed. Please consider changing.

I also think this should be under Numerical integration instead of trying to make it its own topic. WikiMathematician (talk) 19:04, 29 December 2010 (UTC)

References for actual material on page?
I went through the references, and it's not clear that any of the material on the page is substantiated by those references. They provide examples when one might want to use this method, but there is no actual reference to the formulas, especially the formulation for the curse of dimensionality calculation. I would like to see verification of this formulation unless the author of this page is claiming to have come up with it himself. WikiMathematician (talk) 20:02, 29 December 2010 (UTC)

Curse of dimensionality
The sentence "Even with today's computational power it is not possible to process functions with more than 4 or 5 dimensions." needs to be specified. There are ton's of papers concerning different aspects of high-dimensional function "processing", of which the two main sub-cases are approximation and interpolation (as far as I know). --Das O2 (talk) 12:38, 23 January 2018 (UTC)