Error estimates for some quadrature rules with maximal trigonometric degree of exactness

2013 ◽  
Vol 37 (11) ◽  
pp. 1687-1699
Author(s):  
Marija P. Stanić ◽  
Aleksandar S. Cvetković ◽  
Tatjana V. Tomović
Keyword(s):  
Error Estimates ◽  
Quadrature Rules ◽  
Degree Of Exactness

scholarly journals Quadrature rules with an even number of multiple nodes and a maximal trigonometric degree of exactness

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2239-2255 ◽  
Author(s):  
Tatjana Tomovic ◽  
Marija Stanic
Keyword(s):  
Numerical Method ◽  
Trigonometric Polynomials ◽  
Quadrature Rules ◽  
Numerical Examples ◽  
Degree Of Exactness ◽  
Interpolatory Quadrature

This paper is devoted to the interpolatory quadrature rules with an even number of multiple nodes, which have the maximal trigonometric degree of exactness. For constructing of such quadrature rules we introduce and consider the so-called s- and ?-orthogonal trigonometric polynomials. We present a numerical method for construction of mentioned quadrature rules. Some numerical examples are also included.

scholarly journals Rational averaged gauss quadrature rules

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 379-389
Author(s):  
Lothar Reichel ◽  
Miodrag Spalevic ◽  
Jelena Tomanovic
Keyword(s):  
Error Estimates ◽  
Gauss Quadrature ◽  
Quadrature Rules ◽  
Quadrature Error ◽  
Gauss Quadrature Rules

It is important to be able to estimate the quadrature error in Gauss rules. Several approaches have been developed, including the evaluation of associated Gauss-Kronrod rules (if they exist), or the associated averaged Gauss and generalized averaged Gauss rules. Integrals with certain integrands can be approximated more accurately by rational Gauss rules than by Gauss rules. This paper introduces associated rational averaged Gauss rules and rational generalized averaged Gauss rules, which can be used to estimate the error in rational Gauss rules. Also rational Gauss-Kronrod rules are discussed. Computed examples illustrate the accuracy of the error estimates determined by these quadrature rules.

Error bounds for some quadrature rules with maximal trigonometric degree of exactness

2012 ◽  
Author(s):  
Marija P. Stanić ◽  
Aleksandar S. Cvetković ◽  
Tatjana V. Tomović
Keyword(s):  
Error Bounds ◽  
Quadrature Rules ◽  
Degree Of Exactness

scholarly journals Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with Lp–error estimates

2018 ◽  
Vol 4 (2) ◽  
pp. 94-109
Author(s):  
M.W. Alomari
Keyword(s):  
Error Estimates ◽  
Bounded Variation ◽  
Quadrature Rules ◽  
Stieltjes Integral ◽  
Hölder Condition ◽  
Sharp Error

AbstractIn this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral $\int_a^b {f(t)} \,du\,(t)$, where the integrand f is assumed to be satisfied with the Hölder condition on [a, b] and the integrator u is of bounded variation on [a, b]. The dual formulas under the same assumption are proved. Some sharp error Lp–Error estimates for the proposed quadrature rules are also obtained.

scholarly journals Lp –Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

2018 ◽  
Vol 4 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Mohammad W. Alomari ◽  
Allal Guessab
Keyword(s):  
Error Estimates ◽  
Error Bounds ◽  
Quadrature Rules

AbstractIn this work, Lp-error estimates of general two and three point quadrature rules for Riemann-Stieltjes integrals are given. The presented proofs depend on new triangle type inequalities of Riemann-Stieltjes integrals.

scholarly journals Error estimates for certain cubature formulae

Filomat ◽  
2018 ◽  
Vol 32 (20) ◽  
pp. 6893-6902
Author(s):  
Davorka Jandrlic ◽  
Miodrag Spalevic ◽  
Jelena Tomanovic
Keyword(s):  
Error Estimates ◽  
Cubature Formula ◽  
Gaussian Quadrature ◽  
Numerical Procedure ◽  
Quadrature Rule ◽  
Gauss Quadrature ◽  
Quadrature Rules ◽  
The Difference ◽  
Gauss Quadrature Rules ◽  
Cubature Formulae

We estimate the errors of selected cubature formulae constructed by the product of Gauss quadrature rules. The cases of multiple and (hyper-)surface integrals over n-dimensional cube, simplex, sphere and ball are considered. The error estimates are obtained as the absolute value of the difference between cubature formula constructed by the product of Gauss quadrature rules and cubature formula constructed by the product of corresponding Gauss-Kronrod or corresponding generalized averaged Gaussian quadrature rules. Generalized averaged Gaussian quadrature rule ?2l+1 is (2l + 1)-point quadrature formula. It has 2l + 1 nodes and the nodes of the corresponding Gauss rule Gl with l nodes form a subset, similar to the situation for the (2l + 1)-point Gauss-Kronrod rule H2l+1 associated with Gl. The advantages of bG2l+1 are that it exists also when H2l+1 does not, and that the numerical construction of ?2l+1, based on recently proposed effective numerical procedure, is simpler than the construction of H2l+1.

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