Abstract
Generalized Routh-Hurwitz conditions consist of the positivity of $n$determinants associated to a polynomial of degree $n$. They can be used in order toguarantee that a refinable function with dilation $M$ is a ripplet, that is, thecollocation matrices of its shifts are totally positive. Given a polynomial ofdegree$n$, a test of$\mathcal O(n^2)$ elementary operations and growth factor 1 is presented in order tocheck the generalized Routh-Hurwitz conditions. The case corresponding to $M=3$ isdescribed in detail.
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