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

2022/03/07 by Hermoso, Carlos, Huertas, Edmundo J., Lastra, Alberto +1 · 1 citation
#15A23 (Secondary) #33C45 #33C47 (Primary) 42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2203.03318

Abstract

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.

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• Three-term Recurrence Relation with Arbitrary Degree Steps for Orthogonal Polynomials

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