TY  - JOUR
AU  - Milovanović, Gradimir
AU  - Spalević, Miodrag
PY  - 2006
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5072
AB  - We present a method based on the Chakalov–Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules, Numer. Algorithms 10 (1995), 27–39; Quadrature rules based on 
s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhäuser, Basel, 1999, pp. 109–119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.
PB  - Elsevier
T2  - Journal of Computational and Applied Mathematics
T1  - Quadrature rules with multiple nodes for evaluating integrals with strong singularities
EP  - 702
IS  - 1-2
SP  - 689
VL  - 189
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5072
ER  - 

@article{
author = "Milovanović, Gradimir and Spalević, Miodrag",
year = "2006",
abstract = "We present a method based on the Chakalov–Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules, Numer. Algorithms 10 (1995), 27–39; Quadrature rules based on 
s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhäuser, Basel, 1999, pp. 109–119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.",
publisher = "Elsevier",
journal = "Journal of Computational and Applied Mathematics",
title = "Quadrature rules with multiple nodes for evaluating integrals with strong singularities",
pages = "702-689",
number = "1-2",
volume = "189",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5072"
}

Milovanović, G.,& Spalević, M.. (2006). Quadrature rules with multiple nodes for evaluating integrals with strong singularities. in Journal of Computational and Applied Mathematics
Elsevier., 189(1-2), 689-702.
https://hdl.handle.net/21.15107/rcub_machinery_5072

Milovanović G, Spalević M. Quadrature rules with multiple nodes for evaluating integrals with strong singularities. in Journal of Computational and Applied Mathematics. 2006;189(1-2):689-702.
https://hdl.handle.net/21.15107/rcub_machinery_5072 .

Milovanović, Gradimir, Spalević, Miodrag, "Quadrature rules with multiple nodes for evaluating integrals with strong singularities" in Journal of Computational and Applied Mathematics, 189, no. 1-2 (2006):689-702,
https://hdl.handle.net/21.15107/rcub_machinery_5072 .

TY  - JOUR
AU  - Milovanović, Gradimir
AU  - Spalević, Miodrag
AU  - Pranić, Miroslav
PY  - 2005
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5126
T2  - Facta Universitatis, Series: Mathematics and Informatics
T1  - Maximum of the modulus of kernels in Gauss-Turan quadratures with Chebyshev weights: The case s = 1, 2
EP  - 128
SP  - 123
VL  - 20
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5126
ER  - 

@article{
author = "Milovanović, Gradimir and Spalević, Miodrag and Pranić, Miroslav",
year = "2005",
journal = "Facta Universitatis, Series: Mathematics and Informatics",
title = "Maximum of the modulus of kernels in Gauss-Turan quadratures with Chebyshev weights: The case s = 1, 2",
pages = "128-123",
volume = "20",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5126"
}

Milovanović, G., Spalević, M.,& Pranić, M.. (2005). Maximum of the modulus of kernels in Gauss-Turan quadratures with Chebyshev weights: The case s = 1, 2. in Facta Universitatis, Series: Mathematics and Informatics, 20, 123-128.
https://hdl.handle.net/21.15107/rcub_machinery_5126

Milovanović G, Spalević M, Pranić M. Maximum of the modulus of kernels in Gauss-Turan quadratures with Chebyshev weights: The case s = 1, 2. in Facta Universitatis, Series: Mathematics and Informatics. 2005;20:123-128.
https://hdl.handle.net/21.15107/rcub_machinery_5126 .

Milovanović, Gradimir, Spalević, Miodrag, Pranić, Miroslav, "Maximum of the modulus of kernels in Gauss-Turan quadratures with Chebyshev weights: The case s = 1, 2" in Facta Universitatis, Series: Mathematics and Informatics, 20 (2005):123-128,
https://hdl.handle.net/21.15107/rcub_machinery_5126 .