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Refinable functions with general dilation and a stable test for generalized Routh-Hurwitz conditions

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

    Mathematics Subject Classification: Primary: 42C40; Secondary: 26C10, 65G50.


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