Abstract
A classical way to construct a quadrature formula is to approximate the integral \(\int\limits_a^b {f\left( t \right)} \)dt by \(\int\limits_a^b {H\left( {,f;t} \right)dt} \) where H(x, f; t) is the Hermite interpolation polynomial for the function f based on a given system of nodes x = {(x1, v1),..., (xn, vn)} (i.e. x1,...,xn of multiplicities v1,...,vn, respectively). The error E(x; f) of this quadrature rule is expressed by the divided difference f[x,x] of f at the points x and x. We have
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References
Barrow, D., On multiple node Gaussian quadrature formulae. Math. Comp. 32 (1978), 431–439.
Bojanov, B.D., Extremal problems in the set of polynomials with fixed multiplicities of zeros. Comp. Rend. Acad. Bulgare Sci. 31 (1978), 377–400.
Bojanov, B.D., A generalization of Chebyshev polynomials. J. Approximation Theory 26 (1979), 293–300.
Schwartz, J.T., Nonlinear Functional Analysis. Gordon and Breach, New York, 1969.
Tschakaloff, L., General quadrature formulae of Gaussian type, Bulgar. Akad. Nauk Izv. Mat. Inst. 1,2 (1954), 67–84.
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Bojanov, B. (1982). Oscillating Polynomials of Least L1-Norm. In: Hämmerlin, G. (eds) Numerical Integration. ISNM 57: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 57. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6308-7_2
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DOI: https://doi.org/10.1007/978-3-0348-6308-7_2
Publisher Name: Birkhäuser, Basel
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