Point Estimation Theory

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.

REFERENCES:

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.