Timeline for Convergence of integral operators' inverses

8 events

when toggle format	what		by	license	comment
Apr 19 at 21:46	history	edited	tsnao	CC BY-SA 4.0	added 638 characters in body
Apr 19 at 14:21	comment	added	tsnao		@IosifPinelis, a simple model example is when $K$ is the covariance operator of a Brownian motion ($K(x, y) = \min(x, y)$). Then $K^{-1/2}$ is the derivative operator and $K_n^{-1/2}$ is something like discrete derivative.
Apr 19 at 14:14	comment	added	Iosif Pinelis		In order to get $K_n\approx K$, the uniform probability distribution on the set of the $x_i$'s should be close to the uniform distribution over $[0,1]$. So, the grid should be approximately uniform. But, of course, this does not matter to you.
Apr 19 at 13:33	comment	added	tsnao		Although my intuition tells me that it shouldn't matter since the kernel is continuous. But I may be wrong and in the end it's not that important.
Apr 19 at 13:31	history	edited	tsnao	CC BY-SA 4.0	deleted 44 characters in body
Apr 19 at 13:30	comment	added	tsnao		Maybe you're right. Since general grid is not what I'm after, I'll just add an assumption to the question. Thanks!
Apr 19 at 13:17	comment	added	Iosif Pinelis		If the grid is not uniform (or something like that), I think you cannot even even get $K_n\approx K$.
Apr 19 at 13:04	history	asked	tsnao	CC BY-SA 4.0