Calculation of Gaussian quadratures with multiple nodes
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2004
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Metapodaci
Prikaz svih podataka o dokumentuApstrakt
A new algorithm for constructing quadrature formulas with multiple Gaussian nodes
in the presence of certain fixed nodes is presented. It can be used in construction for measures with the bounded and infinite supports. The algorithm includes a simple and fast method for finding elements of the Jacobian matrix in an iterative process with quadratic convergence, which is based on using the fundamental three-term recurrence relation for the corresponding orthogonal polynomials with respect to a given measure. Numerical experiments with respect to several different measures are also included. Finally, a simple method for calculating weight coefficients (Cotes numbers of higher order) of Gaussian and prescribed nodes is presented. Numerical examples are included.
Ključne reči:
Quadratures with multiple nodes / Gauss-Turan-type quadratures / Orthogonal poly- nomials / s- and a-orthogonal polynomials / Zero distribution / Nonnegative measure / Weights / Degree of precision / MomentsIzvor:
MATHEMATICAL AND COMPUTER MODELLING, 2004, 39, 325-347Izdavač:
- Elsevier
Finansiranje / projekti:
- Serbian Ministry of Science, Technology and Development (project No. 2002: Applied Orthogonal Systems, Constructive Approximation and Numerical hlethods)
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Milovanović, Gradimir AU - Spalević, Miodrag AU - Cvetković, Aleksandar PY - 2004 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5066 AB - A new algorithm for constructing quadrature formulas with multiple Gaussian nodes in the presence of certain fixed nodes is presented. It can be used in construction for measures with the bounded and infinite supports. The algorithm includes a simple and fast method for finding elements of the Jacobian matrix in an iterative process with quadratic convergence, which is based on using the fundamental three-term recurrence relation for the corresponding orthogonal polynomials with respect to a given measure. Numerical experiments with respect to several different measures are also included. Finally, a simple method for calculating weight coefficients (Cotes numbers of higher order) of Gaussian and prescribed nodes is presented. Numerical examples are included. PB - Elsevier T2 - MATHEMATICAL AND COMPUTER MODELLING T1 - Calculation of Gaussian quadratures with multiple nodes EP - 347 SP - 325 VL - 39 DO - 10.1016/S0895-7177(04)90014-3 ER -
@article{ author = "Milovanović, Gradimir and Spalević, Miodrag and Cvetković, Aleksandar", year = "2004", abstract = "A new algorithm for constructing quadrature formulas with multiple Gaussian nodes in the presence of certain fixed nodes is presented. It can be used in construction for measures with the bounded and infinite supports. The algorithm includes a simple and fast method for finding elements of the Jacobian matrix in an iterative process with quadratic convergence, which is based on using the fundamental three-term recurrence relation for the corresponding orthogonal polynomials with respect to a given measure. Numerical experiments with respect to several different measures are also included. Finally, a simple method for calculating weight coefficients (Cotes numbers of higher order) of Gaussian and prescribed nodes is presented. Numerical examples are included.", publisher = "Elsevier", journal = "MATHEMATICAL AND COMPUTER MODELLING", title = "Calculation of Gaussian quadratures with multiple nodes", pages = "347-325", volume = "39", doi = "10.1016/S0895-7177(04)90014-3" }
Milovanović, G., Spalević, M.,& Cvetković, A.. (2004). Calculation of Gaussian quadratures with multiple nodes. in MATHEMATICAL AND COMPUTER MODELLING Elsevier., 39, 325-347. https://doi.org/10.1016/S0895-7177(04)90014-3
Milovanović G, Spalević M, Cvetković A. Calculation of Gaussian quadratures with multiple nodes. in MATHEMATICAL AND COMPUTER MODELLING. 2004;39:325-347. doi:10.1016/S0895-7177(04)90014-3 .
Milovanović, Gradimir, Spalević, Miodrag, Cvetković, Aleksandar, "Calculation of Gaussian quadratures with multiple nodes" in MATHEMATICAL AND COMPUTER MODELLING, 39 (2004):325-347, https://doi.org/10.1016/S0895-7177(04)90014-3 . .