= Q-linear convergence
{c}
{title2=$\limsup_k\|e_{k+1}\|/\|e_k\|<1$}
A sequence with errors $e_k=x_k-x^*$ converges Q-linearly in a specified norm if there is a constant $q<1$ with $\|e_{k+1}\|\leq q\|e_k\|$ eventually. The limsup of consecutive nonzero error ratios is its asymptotic factor. This is stronger than merely having a bound $\|e_k\|\leq Cq^k$, which is called R-linear convergence. The norm and whether an iteration is one coordinate step or an entire sweep must be specified when quoting a factor.
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