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

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 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

Nonstandard Gaussian quadrature formulae based on operator values

2009 ◽  
Vol 32 (4) ◽  
pp. 431-486 ◽  
Author(s):  
Gradimir V. Milovanović ◽  
Aleksandar S. Cvetković
Keyword(s):  
Gaussian Quadrature ◽  
Quadrature Formulae
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