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
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by C. Díaz-Mendoza, P. González-Vera and M. Jiménez-Paiz PDF

Math. Comp. 74 (2005), 1843-1870 Request permission

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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