Bracketing Methods

Updated 21 Sep 2026

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What it is
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  root-finding methods that preserve an interval enclosing at least one root
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Sufficient condition
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  if $f$ is continuous on $a,b$ and $f(a)f(b)<0$ , at least one root lies between the endpoints
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Update
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  check endpoint roots first
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  compute a candidate $c$
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  if $f(c)=0$ , stop
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  if $f(a)f(c)>0$ , replace $a$ with $c$
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  otherwise replace $b$ with $c$
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Caution
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  a sign change across a discontinuity does not establish a root
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  some roots do not cause a sign change, such as $f(x)=x^2$ at zero
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  in software, comparing signs avoids unnecessary multiplication that can overflow or underflow
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Related
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  Bisection Method
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  Regula Falsi Method

Linked references 3