Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations

It is well known that Sobolev-type orthogonal polynomials with respect to measures supported on the real line satisfy higher-order recurrence relations and these can be expressed as a (2N + 1)-banded symmetric semi-infinite matrix. In this paper, we state the connection between these (2N + 1)-banded matrices and the Jacobi matrices associated with the three-term recurrence relation satisfied by the standard sequence of orthonormal polynomials with respect to the 2-iterated Christoffel transformation of the measure.

Automated summary

This paper discusses the higher-order recurrence relations satisfied by Sobolev-type orthogonal polynomials and their connection with (2N + 1)-banded symmetric semi-infinite matrices. It also explores the relationship between these matrices and the Jacobi matrices associated with the three-term recurrence relation of standard orthonormal polynomials.