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amelius

I think there is a problem with this technique.

Computing a kernel is an inverse problem, which is more difficult than solving a system for a given right-hand-side.

Linear algebra tells us to never invert a matrix, and here we're actually fabricating the inverse physically.

Or, of course, perhaps I'm misunderstanding something.

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You solve the inverse problem once. That’s takes a while.

Then you build it. More time.

Then you run it for thousands of different inputs. There’s the benefit.

For example:

You build a kernel describing the acoustics of a sound (ie a body of water) once.

Then you can solve instantly what and where sounds (acoustics) are coming from

Well, if the inverse is dense and the excitation as well, then I can see an advantage, because computing a solution by applying the inverse to the excitation would be O(n^2). But I suppose that usually the excitation would be sparse.

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