Regula Falsi Method

Updated 21 Sep 2026

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

Linked references 4