A note on the Geronimus transformation and Sobolev orthogonal polynomials

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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Veröffentlicht in:Numerical algorithms 2014-10, Vol.67 (2), p.271-287
Hauptverfasser: Derevyagin, Maxim, Marcellán, Francisco
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algorithms
Computer Science
Numeric Computing
Numerical Analysis
Original Paper
Polynomials
Symmetry
Theory of Computation
Transformations
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Beschreibung
Zusammenfassung: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-013-9788-6