Error bounds for Gauss-Kronrod quadrature formulae of analytic functions

1993 ◽  
Vol 64 (1) ◽  
pp. 371-380 ◽  
Author(s):  
Sotirios E. Notaris
Keyword(s):  
Error Bounds ◽  
Analytic Functions ◽  
Quadrature Formulae

scholarly journals Error bounds for Gauss-Turán quadrature formulae of analytic functions

2003 ◽  
Vol 72 (244) ◽  
pp. 1855-1873 ◽  
Author(s):  
Gradimir V. Milovanović ◽  
Miodrag M. Spalević
Keyword(s):  
Error Bounds ◽  
Analytic 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 Errors of Gauss-Radau and Gauss-Lobatto quadratures with double end point

2019 ◽  
Vol 13 (2) ◽  
pp. 463-477
Author(s):  
Aleksandar Pejcev ◽  
Ljubica Mihic
Keyword(s):  
Explicit Expression ◽  
Error Bounds ◽  
Analytic Functions ◽  
Remainder Term ◽  
Quadrature Rules ◽  
Quadrature Formulas ◽  
End Points ◽  
End Point ◽  
Appl Math

Starting from the explicit expression of the corresponding kernels, derived by Gautschi and Li (W. Gautschi, S. Li: The remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadrature rules with multiple end points, J. Comput. Appl. Math. 33 (1990) 315{329), we determine the exact dimensions of the minimal ellipses on which the modulus of the kernel starts to behave in the described way. The effective error bounds for Gauss- Radau and Gauss-Lobatto quadrature formulas with double end point(s) are derived. The comparisons are made with the actual errors.

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