With this in mind, there are numerous ways to evaluate the action of K approximately, using discrete methods for approximating the solution of Poisson's equation. For example, the multigrid method can be used to do this in a very efficient way. The analogy with quadrature suggests using a grid with q points and solving Poisson's equation, with a multigrid method in O(q) work. Then the complete evaluation could be done in O(qmn) work. This potentially would be faster than direct evaluation of the integrals.
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