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

• Autores: Juan Manuel Peña Fernández
• Localización: Pre-publicaciones del Seminario Matemático " García de Galdeano ", Nº. 5, 2007
• Idioma: inglés
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• Resumen

  • 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 O(n2) 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.