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

J. M. Peña

doi:10.3934/cpaa.2007.6.809

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2007, Volume 6, Issue 3: 809-818. Doi: 10.3934/cpaa.2007.6.809

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

J. M. Peña¹

1.
Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza

Received: April 2006

Revised: January 2007

Published: August 2007

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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 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.

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

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