On the unbounded divergence of interpolatory product quadrature rules on Jacobi nodes
Keywords:
Product quadrature formulas, superdense sets, condensation of singularities.Abstract
This paper is devoted to prove the unbounded divergence on superdense sets, with respect to product quadrature formulas of interpolatory type on Jacobi nodes.
Mathematics Subject Classification (2010): 41A10, 41A55, 65D32.
References
Brass, H., Petras, K., Quadrature Theory. The theory of Numerical Integration on a Compact Interval, Amer. Math. Soc., Providence, Rhode Island, 2011.
Cobza_s, S., Muntean, I., Condensation of Singularities and Divergence Results in Approximation Theory, J. Approx. Theory, 31(1981), 138-153.
de la Calle Ysern, B., Peherstorfer, F., Ultraspherical Stieltjes Polynomials and Gauss Kronrod Quadrature behave nicely for α < 0, SIAM J. Numer. Anal., 45(2007), 770-786.
Ehrich, S., On product integration with Gauss-Kronrod nodes, SIAM J. Numer. Anal., 35(1998), 78-92.
Mitrea, A.I., On the topological structure of the set of singularities for interpolatory product integration rules, Carpat. J. Math., 30(2014), no. 3, 355-360.
Mitrea, A.I., Double condensation of singularities for product-quadrature formulas with differentiable functions, Carpat. J. Math., 28(2012), no. 1, 83-91.
Nevai, G.P., Mean convergence of Lagrange interpolation, I, J. Approx. Theory, 18(1976), 363-377.
Rabinowitz, P., Smith, W.E., Interpolatory product integration for Riemann-integrable functions, J. Austral. Math. Soc. Ser. B, 29(1987), 195-202.
Sloan, I.H., Smith, W.E., Properties of interpolatory product integration rules, SIAM J. Numer. Anal., 19(1982), 427-442.
Szego, G., Orthogonal Polynomials, Amer. Math. Soc. Providence, 1975.
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