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1. Linear Convergence

   Linked via "sequence (mathematical objects)"

   Linear convergence, often denoted by an order of convergence $\rho = 1$, describes the asymptotic behavior of a sequence (approximation)/) where the error term decreases by a constant multiplicative factor at each successive iteration. Formally, if $a_k$ is the sequence of approximations to a limit $L$, linear convergence implies the existence of a constant $C$ such that $0 < C < 1$ and
   $$\lim{k \to \infty} \frac{|a{k+1} - L|}{|a_k - L|} = C$$
   This constant $C$ is known as the asymptotic convergence factor or rate constant. While mathematically precis…