= Interpolation
{title2=$g(x_i)=y_i$}
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Interpolation constructs a <function> agreeing exactly with prescribed values at sample points. The resulting function is an <interpolant>. Choosing a family determines how missing values are filled: <polynomial interpolation> selects a <polynomial>, while <linear interpolation> joins adjacent samples by straight segments. The <McShane extension theorem> instead permits any <Lipschitz function> with a specified bound and provides envelopes controlling all allowed choices.
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