Regula Falsi Method

Updated 21 Sep 2026

•
What it is
- •
  also called the false-position method; chooses the x-intercept of the line joining the bracket's endpoint values
•
Formula
- •
  $c=b-f(b)\dfrac{b-a}{f(b)-f(a)}$
•
Procedure
- •
  use the sign-preserving update from Bracketing Methods
•
Example
- •
  $f(x)=x^2-2$ , initial bracket $1,2$
- •
  $c_1=4/3$ , $f(c_1)=-2/9$
- •
  $c_2=7/5=1.4$ , $f(c_2)=-1/25$
- •
  $c_3=24/17\approx1.411765$ , $f(c_3)=-2/289$
•
Tradeoff
- •
  uses function magnitudes and may improve faster than bisection
- •
  one endpoint can remain fixed for many iterations, causing slow progress
•
Distinguish from
- •
  the secant method uses a similar interpolation formula but does not preserve a sign-changing bracket
•
Caution
- •
  do not assume bisection’s “width halves every step” error bound applies
•
Related
- •
  Bisection Method

Linked references 2