A theory of constructing initial conditions that provides safe convergence of a numerical root-finding algorithm for an equation . Point estimation theory treats convergence conditions
and the domain of convergence using only information about at the initial point (Petković et al. 1997, p. 1). 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.
Lehmann, E. L. and Casella, G. Theory of Point Estimation. New York: Springer-Verlag, 1998.Petković,
M. S.; Herceg, D. D.; and Ilić, S. M. Point Estimation Theory
and Its Applications. Novi Sad, Yugoslavia: Institute of Mathematics, 1997.
. Point estimation theory treats convergence conditions
and the domain of convergence using only information about 
at the initial point 
(Petković et al. 1997, p. 1). An initial
point that provides safe convergence of Newton's method
is called an approximate zero.
