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Briefly, referencing the Julia documentation on linear algebra subroutines, they note that the Bunch-Kaufman factorization method is more appropriate for symmetric matrices.(old source from NASA) It may go without saying that positive definite matrices are a subset of symmetric matrices, so while Bunch-Kaufman factorization is an improvement, it isn't ...


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The other person's argument sounds to me like a reorganization of your algorithm. It will produce slightly different results, but in the end achieve the same goal. Let me demonstrate with a simple tree of one parent of radius 1, two children of radii (alpha=)0.3 and (beta=)0.7 against a threshold of 0.5. Your suggestion would produce the tree below 1 ...


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I've put together a graphical, non-mathematical explanation of the fast multipole method here. The animations help a lot, but in words: the fast multipole method would be a lot less scary if it were called 'the recursive approximation method'. It constructs a hierarchy of approximations to the field you're trying to calculate, and uses the big approximations ...


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