The Remez multiple exchange algorithm works by moving the frequency samples each iteration to points of maximum error (on a denser grid). Remez iterations could be added to our formulation as well. The Remez multiple exchange algorithm (function firpm [formerly remez] in the Matlab Signal Processing Toolbox, and still remez in Octave) is normally faster than a linear programming formulation, which can be regarded as a single exchange method [#!RabinerAndGold!#, p. 140]. Another reason for the speed of firpm is that it solves the following equations non-iteratively for the filter exhibiting the desired error alternation over the current set of extremal frequencies:
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