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Orthogonal Laurent polynomials corresponding to certain strong Stieltjes distributions with applications to numerical quadratures
Author(s):
C.
Díaz-Mendoza;
P.
González-Vera;
M.
Jiménez
Paiz;
F.
Cala
Rodríguez.
Journal:
Math. Comp.
75
(2006),
281-305.
MSC (2000):
Primary 41A21, 30E05
Posted:
September 9, 2005
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Abstract:
In this paper we shall be mainly concerned with sequences of orthogonal Laurent polynomials associated with a class of strong Stieltjes distributions introduced by A.S. Ranga. Algebraic properties of certain quadratures formulae exactly integrating Laurent polynomials along with an application to estimate weighted integrals on ![$[-1,1]$](/mcom/2006-75-253/S0025-5718-05-01781-3/gif-abstract0/img1.gif) with nearby singularities are given. Finally, numerical examples involving interpolatory rules whose nodes are zeros of orthogonal Laurent polynomials are also presented.
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Additional Information:
C.
Díaz-Mendoza
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna 38271 La Laguna, Tenerife, Canary Islands, Spain
Email:
cjdiaz@ull.es
P.
González-Vera
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna 38271 La Laguna, Tenerife, Canary Islands, Spain
Email:
pglez@ull.es
M.
Jiménez
Paiz
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna 38271 La Laguna, Tenerife, Canary Islands, Spain
Email:
mjimenez@ull.es
F.
Cala
Rodríguez
Affiliation:
Centro de Docencia Superior en Ciencias Básicas, Campus Puerto Montt, Universidad Austral de Chile, Puerto Montt, Chile
Email:
fcala@uach.cl
DOI:
10.1090/S0025-5718-05-01781-3
PII:
S 0025-5718(05)01781-3
Keywords:
Strong Stieltjes distributions,
orthogonal Laurent polynomials,
quadrature formulas,
Stieltjes transform,
two-point Pad\'e approximants
Received by editor(s):
November 4, 2003
Received by editor(s) in revised form:
August 2, 2004
Posted:
September 9, 2005
Additional Notes:
The first three authors were partially supported by the Scientific Research Projects of the Ministerio de Ciencia y Tecnología and Comunidad Autónoma de Canarias under contracts BFM2001-3411 and PI 2002/136, respectively
The work of the fourth author was done during a visit to the Departamento de Análisis Matemático in Universidad de La Laguna (Canary Islands, Spain).
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Copyright
2005,
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