An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the root. In this way, the method of false position keeps the root bracketed (Press et al. 1992).

Using the two-point form of the line

with , using , and solving for  therefore gives the iteration

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 18, 1972.

Chabert, J.-L. (Ed.). "Methods of False Position." Ch. 3 in A History of Algorithms: From the Pebble to the Microchip. New York: Springer-Verlag, pp. 83-112, 1999.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Secant Method, False Position Method, and Ridders' Method." §9.2 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 347-352, 1992.

Whittaker, E. T. and Robinson, G. "The Rule of False Position." §49 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 92-94, 1967.