No not at all. Think for a bit about what the closed form solution of the final generated function is for any of the examples given. Then think of the different

No not at all. Think for a bit about what the closed form solution of the final generated function is for any of the examples given. Then think of the differential equation that it satisfies (with N boundary conditions for every segment of the partition). There's no way solving that is easier than what is done in the article. Even before doing that, there are plenty of other methods that still aren't as efficient, which was one of the main goals of the algorithm.