Superdense unbounded divergence of a class of interpolatory product quadrature formulas

Alexandru Ioan Mitrea

Abstract


Abstract. The aim of this paper is to highlight the superdense unbounded divergence
of a class of product quadrature formulas of interpolatory type on Jacobi
nodes, associated to the Banach space of all real continuous functions defined on
[-1; 1], and to a Banach space of measurable and essentially bounded functions
g : [-1; 1] ! R. Some aspects regarding the convergence of these formulas are
pointed out, too.


Keywords


Superdense set, unbounded divergence, product quadrature formulas, Dini-Lipschitz convergence

Full Text:

PDF

References


Brass, H., Petras, K., Quadrature Theory. The theory of Numerical Integration on a Compact Interval, Amer. Math. Soc., Providence, Rhode Island, 2011.

Cheney, E.W., Light, W.A., A Course on Approximation Theory, Amer. Math. Soc., Providence, Rhode Island, 2009.

Cobzas, S., Muntean, I., Condensation of singularities and divergence results in approximation theory, J. Approx. Theory, 31(1981), 138-153.

Ehrich, S., On product integration with Gauss-Kronrod nodes, SIAM J. Numer. Anal.,35(1998), 78-92.

Mitrea, A.I., On the dense divergence of the product quadrature formulas of interpolatorytype, J. Math. Anal. Appl., 433(2016), 1409-1414.

Natanson, G.I., Two-sided estimates for Lebesgue functions of Lagrange interpolationprocesses based on Jacobi nodes (Russian), Izv. Vyss, Ucehn, Zaved (Mathematica),

(1967), 67-74.

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.

Vertesi, P., Note on mean convergence of Lagrange parabolas, J. Approx. Theory, 28(1980), 30-35.

Szego, G., Orthogonal Polynomials, Amer. Math. Soc., Providence, Rhode Island, 2003.


Refbacks

  • There are currently no refbacks.