Computing the Hessenberg matrix associated with a self-similar measure |
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| Authors: | C Escribano A Giraldo MA Sastre E Torrano |
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| Institution: | Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo, 28660 Boadilla del Monte, Madrid, Spain;Lenguajes y Systemas Informaticos e ingenieria de Software, Facultad de Informatica, Universidad Politecnica de Madrid, Campus de Montegancedo, Boadilla del Monte, Madrid, Spain 28660;Departamento de Matemáticas, Universidad Carlos III de Madrid Escuela Politécnica Superior, Av. Universidad 30 - 28911 LEGANES (Madrid), Spain;Departamento de Estad?´stica y Matemática Aplicada, Edificio CITE III, Desp. 256, Universidad de Almer?´a, 04120 Almer?´a, ESPAÑA (Spain) |
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| Abstract: | We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures.We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures.Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix. |
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