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arXiv · 1603.01986

Alpert multiwavelets and Legendre-Angelesco multiple orthogonal polynomials

Jeffrey S. Geronimo·Plamen Iliev·Walter Van Assche
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Abstract

We show that the multiwavelets, introduced by Alpert in 1993, are related to type I Legendre-Angelesco multiple orthogonal polynomials. We give explicit formulas for these Legendre-Angelesco polynomials and for the Alpert multiwavelets. The multiresolution analysis can be done entirely using Legendre polynomials, and we give an algorithm, using Cholesky factorization, to compute the multiwavelets and a method, using the Jacobi matrix for Legendre polynomials, to compute the matrices in the scaling relation for any size of the multiplicity of the multiwavelets.

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Jeffrey S. Geronimo, Plamen Iliev, Walter Van Assche. 2016-03-07. Alpert multiwavelets and Legendre-Angelesco multiple orthogonal polynomials. https://doi.org/10.1137/16m1064465

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