A note on the Geronimus transformation and Sobolev orthogonal polynomials

In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner products.

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Bibliographic Details
Published in:	Numerical algorithms Vol. 67; no. 2; pp. 271 - 287
Main Authors:	Derevyagin, Maxim, Marcellán, Francisco
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01-10-2014 Springer Nature B.V
Subjects:	Algebra Algorithms Computer Science Numeric Computing Numerical Analysis Original Paper Polynomials Symmetry Theory of Computation Transformations Geronimus transformation Cholesky decomposition Sobolev inner products Secondary 15A23 Orthogonal polynomials Jacobi matrices Primary 42C05
Online Access:	Get full text
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Summary:	In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner products.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	1017-1398 1572-9265
DOI:	10.1007/s11075-013-9788-6