For a 1-dimensional function (''d'' = 1), a δ<math>\delta</math>-absolute fixed-point can be found using <math>O(\log(1/\delta))</math> queries using the [[bisection method]]: start with the interval <math>E := [0, 1]</math>; at each iteration, let ''<math>x''</math> be the center of the current interval, and compute ''<math>f''(''x'')</math>; if ''<math>f''(''x'') > ''x''</math> then recurse on the sub-interval to the right of ''<math>x''</math>; otherwise, recurse on the interval to the left of ''<math>x''</math>. Note that the current interval always contains a fixed point, so after <math>O(\log(1/\delta))</math> queries, any point in the remaining interval is a δ<math>\delta</math>-absolute fixed-point of ''<math>f.''</math> Setting <math>\delta := \varepsilon/(L+1)</math>, where ''<math>L''</math> is the Lipschitz constant, gives an {{mvar|ε}}-residual fixed-point, using <math>O(\log(L/\varepsilon) = \log(L) + \log(1/\varepsilon))</math> queries.<ref name=":0" />
