Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules
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2018
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Modified Stieltjes polynomials are defined and used to construct suboptimal extensions of Gaussian rules with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. We prove that, for wide classes of weight functions and a sufficiently large number of nodes, the extended quadratures have positive weights and simple nodes on the interval . The classes of weight functions considered complement those for which the Gauss-Kronrod rule is known to exist. Also, strong asymptotic representations on the whole interval are given for the modified Stieltjes polynomials, which prove that they behave asymptotically as orthogonal polynomials. Finally, we provide some numerical examples.
Izvor:
Numerische Mathematik, 2018, 138, 1, 1-35Izdavač:
- Springer Heidelberg, Heidelberg
Finansiranje / projekti:
- Metode numeričke i nelinearne analize sa primenama (RS-MESTD-Basic Research (BR or ON)-174002)
- Direccion General de Investigacion [MTM2014-54053-P]
- Universidad Politecnica de Madrid [GI-1505440113
DOI: 10.1007/s00211-017-0901-y
ISSN: 0029-599X
WoS: 000419882800001
Scopus: 2-s2.0-85021204096
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Institucija/grupa
Mašinski fakultetTY - JOUR AU - de la Calle Ysern, B. AU - Spalević, Miodrag PY - 2018 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2944 AB - Modified Stieltjes polynomials are defined and used to construct suboptimal extensions of Gaussian rules with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. We prove that, for wide classes of weight functions and a sufficiently large number of nodes, the extended quadratures have positive weights and simple nodes on the interval . The classes of weight functions considered complement those for which the Gauss-Kronrod rule is known to exist. Also, strong asymptotic representations on the whole interval are given for the modified Stieltjes polynomials, which prove that they behave asymptotically as orthogonal polynomials. Finally, we provide some numerical examples. PB - Springer Heidelberg, Heidelberg T2 - Numerische Mathematik T1 - Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules EP - 35 IS - 1 SP - 1 VL - 138 DO - 10.1007/s00211-017-0901-y ER -
@article{ author = "de la Calle Ysern, B. and Spalević, Miodrag", year = "2018", abstract = "Modified Stieltjes polynomials are defined and used to construct suboptimal extensions of Gaussian rules with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. We prove that, for wide classes of weight functions and a sufficiently large number of nodes, the extended quadratures have positive weights and simple nodes on the interval . The classes of weight functions considered complement those for which the Gauss-Kronrod rule is known to exist. Also, strong asymptotic representations on the whole interval are given for the modified Stieltjes polynomials, which prove that they behave asymptotically as orthogonal polynomials. Finally, we provide some numerical examples.", publisher = "Springer Heidelberg, Heidelberg", journal = "Numerische Mathematik", title = "Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules", pages = "35-1", number = "1", volume = "138", doi = "10.1007/s00211-017-0901-y" }
de la Calle Ysern, B.,& Spalević, M.. (2018). Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules. in Numerische Mathematik Springer Heidelberg, Heidelberg., 138(1), 1-35. https://doi.org/10.1007/s00211-017-0901-y
de la Calle Ysern B, Spalević M. Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules. in Numerische Mathematik. 2018;138(1):1-35. doi:10.1007/s00211-017-0901-y .
de la Calle Ysern, B., Spalević, Miodrag, "Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules" in Numerische Mathematik, 138, no. 1 (2018):1-35, https://doi.org/10.1007/s00211-017-0901-y . .