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1. Sequence

   Linked via "sublinear"

   When a sequence is generated iteratively, the Order of Convergence ($\rho$) quantifies the speed at which the terms approach the limit $L$. It is defined through the asymptotic relationship between successive errors:
   $$\lim{k \to \infty} \frac{|a{k+1} - L|}{|a_k - L|^\rho} = C$$
   Sequences exhibiting higher orders of convergence, such as those arising from Newton's method applied to well-behaved functions ($\rho=2$), typically achieve a specified tolerance far faster than linear ($\rho=1$) or …