= Rational interpolation
{title2=$q(x_i)/r(x_i)=f_i$}
Rational interpolation seeks a <rational function> $q/r$ with prescribed bounds on the <polynomial degrees> of its numerator and denominator and prescribed values at distinct <interpolation nodes>. A <rational interpolant> must have a well-defined value at each <interpolation node>. With a specified numerator-denominator representation, this requires $r(x_i)\ne0$ for every $i$. A normalization such as a <monic polynomial> denominator removes the common scaling freedom but does not guarantee existence or uniqueness. Multiplying by a zero denominator can create spurious solutions to the <rational interpolation linearization>.
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