Bidiagonal factorization of recurrence banded matrices in mixed multiple orthogonality

TL;DR

This paper presents a method to explicitly construct a bidiagonal factorization of the recurrence matrix in mixed multiple orthogonality, utilizing LU factorization and Christoffel transformations to relate to orthogonal polynomials.

Contribution

It introduces a novel explicit construction of the bidiagonal factorization for recurrence matrices in mixed multiple orthogonality using LU and Christoffel transformations.

Findings

Explicit bidiagonal factorization derived for recurrence matrices

Connection established between factorization and orthogonal polynomial coefficients

Method applicable to mixed multiple orthogonality on the step-line

Abstract

This paper demonstrates how to explicitly construct a bidiagonal factorization of the banded recurrence matrix that appears in mixed multiple orthogonality on the step-line in terms of the coeffcients of the mixed multiple orthogonal polynomials. The construction is based on the \(LU\) factorization of the moment matrix and Christoffel transformations applied to the matrix of measures and the associated mixed multiple orthogonal polynomials.