I'm curious as to whether anyone can provide any intuition to me about sparse grid nodes. I am aware that there is a formula that determines the locations of the nodes as a function of the sparse grid level, cf. https://www.encyclopediaofmath.org/index.php/Smolyak_algorithm#References .
However, after doing a somewhat extensive literature review, it is not clear to me as to why the location of the sparse grid nodes needs to be obtained in this manner. Is it just a matter of convenience? Is this simply an algorithm? Or is it because of the sparse grid interpolant?
I'd be very grateful to anyone who can provide some intuition about this as well as good references.