Error bounds for Gaussian quadrature formulae with Bernstein-Szego weights that are rational modifications of Chebyshev weight functions of the second kind

2012 ◽  
Vol 32 (4) ◽  
pp. 1733-1754 ◽  
Author(s):  
A. V. Pejcev ◽  
M. M. Spalevic
Keyword(s):  
Error Bounds ◽  
Gaussian Quadrature ◽  
Weight Functions ◽  
Quadrature Formulae

scholarly journals Error estimates of Gaussian quadrature formulae with the third class of Bernstein-Szegő weights

2017 ◽  
Vol 11 (2) ◽  
pp. 451-469
Author(s):  
Aleksandar Pejcev
Keyword(s):  
Error Estimates ◽  
Error Bounds ◽  
Analytic Functions ◽  
Gaussian Quadrature ◽  
Gauss Quadrature ◽  
Weight Functions ◽  
Quadrature Formulae ◽  
The Third ◽  
Exact Degree ◽  
Gauss Quadrature Rules

For analytic functions we study the remainder terms of Gauss quadrature rules with respect to Bernstein-Szeg? weight functions w(t) = w?,?,?(t) = ?1+t/ 1-t/?(?-2?)t2+2?(?-?)t+?2+?2, t?(-1,1), where 0 < ? < ?, ??2?, ??? < ?-?, and whose denominator is an arbitrary polynomial of exact degree 2 that remains positive on [-1,1]. The subcase ?=1, ?= 2/(1+?), -1 < ? < 0 and ?=0 has been considered recently by M. M. Spalevic, Error bounds of Gaussian quadrature formulae for one class of Bernstein-Szeg? weights, Math. Comp., 82 (2013), 1037-1056.

scholarly journals The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type

2020 ◽  
Vol 369 ◽  
pp. 124806
Author(s):  
Ramón Orive ◽  
Aleksandar V. Pejčev ◽  
Miodrag M. Spalević
Keyword(s):  
Error Bounds ◽  
Gauss Quadrature ◽  
Weight Functions ◽  
Quadrature Formulae

Maximum of the modulus of kernels of Gaussian quadrature formulae for one class of Bernstein–Szegő weight functions

2012 ◽  
Vol 218 (9) ◽  
pp. 5746-5756 ◽  
Author(s):  
Miodrag M. Spalević ◽  
Miroslav S. Pranić ◽  
Aleksandar V. Pejčev
Keyword(s):  
Gaussian Quadrature ◽  
Weight Functions ◽  
Quadrature Formulae

The error bounds of Gauss–Radau quadrature formulae with Bernstein–Szegő weight functions

2015 ◽  
Vol 133 (1) ◽  
pp. 177-201 ◽  
Author(s):  
Aleksandar V. Pejčev ◽  
Miodrag M. Spalević
Keyword(s):  
Error Bounds ◽  
Weight Functions ◽  
Quadrature Formulae

Kronrod Extensions of Gaussian Quadratures with Multiple Nodes

2006 ◽  
Vol 6 (3) ◽  
pp. 291-305 ◽  
Author(s):  
G.V. Milovanović ◽  
M.M. Spalević ◽  
L.J. Galjak
Keyword(s):  
Error Bounds ◽  
Existence And Uniqueness ◽  
Gaussian Quadrature ◽  
Weight Functions ◽  
Quadrature Formulas ◽  
Gaussian Quadrature Formulas ◽  
Gaussian Quadratures ◽  
Explicit Expressions

Abstract In this paper, general real Kronrod extensions of Gaussian quadrature formulas with multiple nodes are introduced. A proof of their existence and uniqueness is given. In some cases, the explicit expressions of polynomials, whose zeros are the nodes of the considered quadratures, are determined. Very effective error bounds of the Gauss — Turán — Kronrod quadrature formulas, with Gori — Micchelli weight functions, for functions analytic on confocal ellipses, are derived.

scholarly journals Error bounds of certain Gaussian quadrature formulae

2010 ◽  
Vol 234 (4) ◽  
pp. 1049-1057 ◽  
Author(s):  
Miodrag M. Spalević ◽  
Miroslav S. Pranić
Keyword(s):  
Error Bounds ◽  
Gaussian Quadrature ◽  
Quadrature Formulae

The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegő type

2017 ◽  
Vol 77 (4) ◽  
pp. 1003-1028
Author(s):  
Dušan Lj. Djukić ◽  
Aleksandar V. Pejčev ◽  
Miodrag M. Spalević
Keyword(s):  
Error Bounds ◽  
Weight Functions ◽  
Quadrature Formulae
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