A theory of constructing initial conditions that provides safe convergence of a numerical root-finding algorithm for an equation f(z) = 0. Point estimation theory treats convergence conditions and the domain of convergence using only information about f at the initial point z_0 . An initial point that provides safe convergence of Newton's method is called an approximate zero. Point estimation theory should not be confused with point estimators of probability theory.

alpha-test | approximate zero | Newton's method | point estimator