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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A Lagrange-type projector on the real line


Authors: G. Mastroianni and I. Notarangelo
Journal: Math. Comp. 79 (2010), 327-352
MSC (2000): Primary 41A05, 65D05, 65D30, 65D32; Secondary 41A10
Published electronically: July 7, 2009
MathSciNet review: 2552229
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Abstract: We introduce an interpolation process based on some of the zeros of the $ m$th generalized Freud polynomial. Convergence results and error estimates are given. In particular we show that, in some important function spaces, the interpolating polynomial behaves like the best approximation. Moreover the stability and the convergence of some quadrature rules are proved.


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Additional Information

G. Mastroianni
Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, V.le dell’Ateneo Lucano 10, I-85100 Potenza, Italy
Email: mastroianni.csafta@unibas.it

I. Notarangelo
Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, V.le dell’Ateneo Lucano 10, I-85100 Potenza, Italy
Email: incoronata.notarangelo@unibas.it

DOI: http://dx.doi.org/10.1090/S0025-5718-09-02278-9
PII: S 0025-5718(09)02278-9
Keywords: Orthogonal polynomials, Lagrange interpolation, quadrature rules
Received by editor(s): March 31, 2008
Received by editor(s) in revised form: March 23, 2009
Published electronically: July 7, 2009
Additional Notes: This research was partially supported by Ministero dell’Università e della Ricerca, PRIN 2006 “Numerical methods for structured linear algebra and applications”.
Dedicated: Dedicated to Professor J. Szabados on the occasion of his 70th birthday
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.