Refinable functions with general dilation and a stable test for generalized Routh-Hurwitz conditions
Juan Manuel Peña · Communications on Pure & Applied Analysis · 2007
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.