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Root Finding

Updated 21 Sep 2026

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What it is
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  finding input $r$ satisfying $f(r)=0$
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Method families
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  bracketing methods - maintain an interval containing a root under appropriate assumptions
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  open methods - generate approximatios without maintaining a sign-changing bracket
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Preparation
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  rewrite the equation as $f(x)=0$
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  consider continuity, domain restrictions, and whether multiple roots may exist
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Stoppign criteria
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  bracket width or an error bound
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  change between successive estimates
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  residual magnitude $|f(x)|$
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  iteration limit
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Caution
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  a small residual does not always imply a small error in $x$
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  the dump names open methods but does not supply their algorithms
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Related
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  Bracketing Methods
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Linked references 1

numerical-methods-polban

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