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Calio, Franca; Frontini, Marco; Milovanović, Gradimir V.

Numerical differentiation of analytic functions using quadratures on the semicircle. (English) Zbl 0752.65015

Comput. Math. Appl. 22, No. 10, 99-106 (1991).
An extension for higher derivatives of Milovanović’s method for the numerical differentiation of analytic functions using Gauss-Christoffel quadrature formulas is presented. Some numerical results are given.
Reviewer: S.Filippi (Gießen)

Cited in 8 Documents

MSC:

65D25 Numerical differentiation

Keywords:

higher derivatives; Milovanović’s method; numerical differentiation; analytic functions; Gauss-Christoffel quadrature formulas; numerical results
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References:

[1] Gautschi, W.; Milovanović, G. V., Polynomials orthogonal on the semicircle, J. Approx. Theor., 46, 230-250 (1986) · Zbl 0604.42024
[2] Gautschi, W.; Landau, H.; Milovanović, G. V., Polynomials orthogonal on the semicircle II, Constr. Approx., 3, 389-404 (1987) · Zbl 0658.42027
[3] Milovanović, G. V., Complex orthogonality on the semicircle with respect to Gegenbauer weight: Theory and applications, (Rassias, Th. M., Topics in Mathematical Analysis (1989), World Scientific: World Scientific Singapore), 695-722 · Zbl 0732.65014
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[8] Tošić, D.Đ.; Elbahi, A. A., Optimal numerical differentiation of real-valued analytic functions, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., No 735-No 762, 122-126 (1982) · Zbl 0538.65008
[9] Golub, G. H.; Welsch, J. H., Calculation of Gauss quadrature rules, Math. Comp., 23, 221-230 (1969) · Zbl 0179.21901
[10] Milovanović, G. V., Some applications of the polynomials orthogonal on the semicircle, (Numerical Methods. Numerical Methods, Colloq. Math. Soc. János Bolyai, Vol. 50 (1987), North-Holland: North-Holland Amsterdam/New York), 625-634, (Miskolc, 1986) · Zbl 0638.65015
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