Alpert Multiwavelets and Legendre--Angelesco Multiple Orthogonal Polynomials
Jeffrey S. Geronimo, Plamen Iliev, Walter Van Assche · SIAM Journal on Mathematical Analysis · 2017
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, for computing the multiwavelets and a method, using the Jacobi matrix for Legendre polynomials, for computing the matrices in the scaling relation for any size of the multiplicity of the multiwavelets.