Superlinear convergence ($\Vert e_{n+1}\Vert /\Vert e_n\Vert ⟶0$)

An iterative sequence converges superlinearly to its limit when its nonzero error norms satisfy the displayed ratio condition, or when it reaches the limit in finitely many steps. Quadratic convergence is a stronger local rate. In contrast, exact linear convergence has a positive asymptotic error ratio below one. A superlinear method need not have quadratic convergence.