Alpert multiwavelets and Legendre-Angelesco multiple orthogonal polynomials
Classical Analysis and ODEs
2017-02-27 v1
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.
Cite
@article{arxiv.1603.01986,
title = {Alpert multiwavelets and Legendre-Angelesco multiple orthogonal polynomials},
author = {Jeffrey S. Geronimo and Plamen Iliev and Walter Van Assche},
journal= {arXiv preprint arXiv:1603.01986},
year = {2017}
}
Comments
19 pages + 7 pages supplementary materials