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

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.

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

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

scholarly journals Stieltjes polynomials and related quadrature formulae for a class of weight functions

1996 ◽  
Vol 65 (215) ◽  
pp. 1257-1269 ◽  
Author(s):  
Walter Gautschi ◽  
Sotirios E. Notaris
Keyword(s):  
Weight Functions ◽  
Quadrature Formulae
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