Strong Stieltjes distributions and orthogonal Laurent polynomials with applications to quadratures and Padé approximation

Díaz-Mendoza, C.; González-Vera, P.; Jiménez-Paiz, M.

doi:10.1090/S0025-5718-05-01763-1

Strong Stieltjes distributions and orthogonal Laurent polynomials with applications to quadratures and Padé approximation

Authors: C. Díaz-Mendoza, P. González-Vera and M. Jiménez-Paiz
Journal: Math. Comp. 74 (2005), 1843-1870
MSC (2000): Primary 42C05, 41A55
DOI: https://doi.org/10.1090/S0025-5718-05-01763-1
Published electronically: June 7, 2005
MathSciNet review: 2164100
Full-text PDF Free Access

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Abstract: Starting from a strong Stieltjes distribution $\phi$ , general sequences of orthogonal Laurent polynomials are introduced and some of their most relevant algebraic properties are studied. From this perspective, the connection between certain quadrature formulas associated with the distribution $\phi$ and two-point Padé approximants to the Stieltjes transform of $\phi$ is revisited. Finally, illustrative numerical examples are discussed.

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