Error Estimates of Product Quadrature Formulae

1993 ◽  
pp. 241-252 ◽  
Author(s):  
Giuseppe Mastroianni ◽  
Péter Vértesi
Keyword(s):  
Error Estimates ◽  
Quadrature Formulae

scholarly journals Monotonicity of the error term in Gauss-Turán quadratures for analytic function

2007 ◽  
Vol 48 (4) ◽  
pp. 567-581 ◽  
Author(s):  
Gradimir V. Milovanović ◽  
Miodrag M. Spalević
Keyword(s):  
Analytic Function ◽  
Weight Function ◽  
Error Estimates ◽  
Complex Plane ◽  
Error Term ◽  
Quadrature Formulae

AbstractFor Gauss–Turán quadrature formulae with an even weight function on the interval [−1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than I, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some ℓ2-error estimates are considered.

Bounds for the Chebyshev functional and corrected four-point quadrature formulae of Euler type

2016 ◽  
Vol 09 (04) ◽  
pp. 1650078
Author(s):  
J. Pečarić ◽  
M. Ribičić Penava
Keyword(s):  
Error Estimates ◽  
Quadrature Formulae ◽  
Chebyshev Functional ◽  
Special Case

The aim of this paper is to consider some new estimations of the reminder in closed corrected four-point quadrature formulae of Euler type using some inequalities for the Chebyshev functional. In special case, we obtain some new bounds for the corrected Euler–Simpson [Formula: see text] formula. Some new error estimates for the corrected Euler–Bullen–Simpson [Formula: see text] formula are derived too.

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