On the computation of Patterson-type quadrature rules
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2022
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We describe a stable and efficient algorithm for computing positive suboptimal extensions of the Gaussian quadrature rule with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. These rules constitute a particular case of those first considered by Begumisa and Robinson (1991) and then by Patterson (1993) and have been proven to verify asymptotically good properties for a large class of weight functions. In particular, they may exist when the Gauss-Kronrod rule does not. The proposed algorithm is a nontrivial modification of the one introduced by Laurie (1997) for the Gauss-Kronrod quadrature, and it is based on the determination of an associated Jacobi matrix. The nodes and weights of the rule are then given as the eigenvalues and eigenvectors of the matrix, as in the classical Golub-Welsch algorithm (1969).
Кључне речи:
Suboptimal rules / Stieltjes polynomials / Stable numerical method / Patterson quadrature rules / Gauss-Kronrod quadratureИзвор:
Journal of Computational and Applied Mathematics, 2022, 403Издавач:
- Elsevier, Amsterdam
DOI: 10.1016/j.cam.2021.113850
ISSN: 0377-0427
WoS: 000710203600018
Scopus: 2-s2.0-85117386863
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Институција/група
Mašinski fakultetTY - JOUR AU - Calle Ysern, Bernardo de la AU - Spalević, Miodrag PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3747 AB - We describe a stable and efficient algorithm for computing positive suboptimal extensions of the Gaussian quadrature rule with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. These rules constitute a particular case of those first considered by Begumisa and Robinson (1991) and then by Patterson (1993) and have been proven to verify asymptotically good properties for a large class of weight functions. In particular, they may exist when the Gauss-Kronrod rule does not. The proposed algorithm is a nontrivial modification of the one introduced by Laurie (1997) for the Gauss-Kronrod quadrature, and it is based on the determination of an associated Jacobi matrix. The nodes and weights of the rule are then given as the eigenvalues and eigenvectors of the matrix, as in the classical Golub-Welsch algorithm (1969). PB - Elsevier, Amsterdam T2 - Journal of Computational and Applied Mathematics T1 - On the computation of Patterson-type quadrature rules VL - 403 DO - 10.1016/j.cam.2021.113850 ER -
@article{ author = "Calle Ysern, Bernardo de la and Spalević, Miodrag", year = "2022", abstract = "We describe a stable and efficient algorithm for computing positive suboptimal extensions of the Gaussian quadrature rule with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. These rules constitute a particular case of those first considered by Begumisa and Robinson (1991) and then by Patterson (1993) and have been proven to verify asymptotically good properties for a large class of weight functions. In particular, they may exist when the Gauss-Kronrod rule does not. The proposed algorithm is a nontrivial modification of the one introduced by Laurie (1997) for the Gauss-Kronrod quadrature, and it is based on the determination of an associated Jacobi matrix. The nodes and weights of the rule are then given as the eigenvalues and eigenvectors of the matrix, as in the classical Golub-Welsch algorithm (1969).", publisher = "Elsevier, Amsterdam", journal = "Journal of Computational and Applied Mathematics", title = "On the computation of Patterson-type quadrature rules", volume = "403", doi = "10.1016/j.cam.2021.113850" }
Calle Ysern, B. d. l.,& Spalević, M.. (2022). On the computation of Patterson-type quadrature rules. in Journal of Computational and Applied Mathematics Elsevier, Amsterdam., 403. https://doi.org/10.1016/j.cam.2021.113850
Calle Ysern BDL, Spalević M. On the computation of Patterson-type quadrature rules. in Journal of Computational and Applied Mathematics. 2022;403. doi:10.1016/j.cam.2021.113850 .
Calle Ysern, Bernardo de la, Spalević, Miodrag, "On the computation of Patterson-type quadrature rules" in Journal of Computational and Applied Mathematics, 403 (2022), https://doi.org/10.1016/j.cam.2021.113850 . .