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* If the errors at every <math> m \in M </math> are of equal magnitude and alternate in sign, then <math>P_n</math> is the minimax approximation polynomial. If not, replace ''X'' with ''M'' and repeat the steps above.
The result is called the polynomial of best approximation or the [[minimax approximation algorithm]].
A review of technicalities in implementing the Remez algorithm is given by W. Fraser.<ref>{{cite journal |doi=10.1145/321281.321282 |first=W. |last=Fraser |title=A Survey of Methods of Computing Minimax and Near-Minimax Polynomial Approximations for Functions of a Single Independent Variable |journal=J. ACM |volume=12 |issue= |pages=295 |year=1965 }}</ref>
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