On initialization of Max´s algorithm for optimum quantization

Two methods for initializing J. Max´s (1960) iterative algorithm for optimum quantization for a rapid convergence of the algorithm are derived and tested. The methods, which are based on making an intelligent guess of the starting point, perform considerably better than the existing methods for a wide class of reasonably well-behaved unimodal density functions, while the amount of computations involved is negligible compared with what is involved in a single iteration of Max´s algorithm. An interesting relationship between optimum quantizers of different levels is revealed in the derivation of these methods. This relationship could also be useful for scalar quantizer design