We were introduced to testing the convergence of a series & calculating the point of convergence in the first maths of college curriculum. I wish to explore its usage in computer algorithms.
What I mean is, the testing of convergence (using the different tests) gives an answer of yes | no. Such conclusions can save considerable amounts of computing time (as in algorithms where a no can mean, stop proceeding). I have seen the Taylor series being used in a few algorithms where the point of convergence is to be calculated.
Could anyone point out some real world algorithms where they play major role (e.g., optimization techniques, graphic algorithms, etc).
As Qiaochu Yuan stated in this post, "Mastering the use of Taylor series is already highly nontrivial - especially recognizing when the method is applicable". (Some examples of these non trivial places??)