Does anybody know how difficult these problems are to solve once you've already calculated the relevant kernel? Let's say I had that kernel stored in a databas

Does anybody know how difficult these problems are to solve once you've already calculated the relevant kernel? Let's say I had that kernel stored in a database, is it just a matrix multiplication or two to calculate the solution? If so, doesn't that kind of invalidate the idea that this is a bottleneck problem that requires a speed-up? Especially once you take into account read/write speeds on the physical structure? I guess my point here is the correct benchmark is pre-memoized code. I'd be interested how it performs against that benchmark.