On entry: an absolute tolerance to control the accuracy to which the zero is determined. In general, the smaller the value of
eps the more accurate
x will be as an approximation to
$\alpha $. Indeed, for very small positive values of
eps, it is likely that the final approximation will satisfy
$\left|{\mathbf{x}}-\alpha \right|<{\mathbf{eps}}$. You are advised to call the function with more than one value for
eps to check the accuracy obtained.