I suspect whoever wrote this Wikipedia sentence didn't use the words in the way I think they should mean. What does is mean for a pair of distinct sequences to "be the same algebraically" here? Obviously they are not identical or this transform wouldn't help accelerate convergence.
https://en.wikipedia.org/wiki/Aitken%27s_delta-squared_process#Definition
Also, it would be really nice if the page had a proof of *why* this works.
h/t @johndcook whose blog post made me look into this.







