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
See also Brent's Method ,
Ridders'
Method ,
Secant Method
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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. Referenced on Wolfram|Alpha Method of False Position
Cite this as:
Weisstein, Eric W. "Method of False Position."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/MethodofFalsePosition.html
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