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The proposed algorithm is totally unrelated to that stated in McKeeman's article. McKeeman subdivides the interval into *three* subintervals, and recurses on them. Further, error estimates are based on some difference between certain estimates, however not on asymptotic expansion, where the 15 in this article stems from. Certainly, this algorithm will work. It's much more straightforward and easier to grasp as McKeeman's is, however, they're not the same.
