An Error Estimate for Stenger's Quadrature Formula

1982 ◽  
Vol 38 (158) ◽  
pp. 539
Author(s):  
S. Beighton ◽  
B. Noble
Keyword(s):  
Error Estimate ◽  
Quadrature Formula

scholarly journals Generalized Simpson type inequalities involving Riemann-Liouville fractional integrals and their applications

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 751-760
Author(s):  
Chunyan Luo ◽  
Tingsong Du
Keyword(s):  
Error Estimate ◽  
Quadrature Formula ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Digamma Function ◽  
Type Identity ◽  
Special Means

We establish a Simpson type identity and several Simpson type inequalities for Riemann-Liouville fractional integrals. As applications, we apply the obtained results to special means of real numbers, an error estimate for Simpson type quadrature formula, and q-digamma function, respectively.

Error estimate and extrapolation of a quadrature formula derived from a quartic spline quasi-interpolant

2010 ◽  
Vol 50 (4) ◽  
pp. 843-862 ◽  
Author(s):  
P. Sablonnière ◽  
D. Sbibih ◽  
M. Tahrichi
Keyword(s):  
Error Estimate ◽  
Quadrature Formula

scholarly journals An error estimate for Stenger’s quadrature formula

1982 ◽  
Vol 38 (158) ◽  
pp. 539-539
Author(s):  
S. Beighton ◽  
B. Noble
Keyword(s):  
Error Estimate ◽  
Quadrature Formula

scholarly journals The Ostrowski inequality for $ s $-convex functions in the third sense

2022 ◽  
Vol 7 (4) ◽  
pp. 5605-5615
Author(s):  
Gültekin Tınaztepe ◽  
◽  
Sevda Sezer ◽  
Zeynep Eken ◽  
Sinem Sezer Evcan ◽  
...  
Keyword(s):  
Error Estimate ◽  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Power Mean ◽  
Ostrowski Inequality ◽  
Riemann Sums ◽  
The Third ◽  
The Absolute

<abstract><p>In this paper, the Ostrowski inequality for $ s $-convex functions in the third sense is studied. By applying Hölder and power mean integral inequalities, the Ostrowski inequality is obtained for the functions, the absolute values of the powers of whose derivatives are $ s $-convex in the third sense. In addition, by means of these inequalities, an error estimate for a quadrature formula via Riemann sums and some relations involving means are given as applications.</p></abstract>

QMC integration errors and quasi-asymptotics

2020 ◽  
Vol 26 (3) ◽  
pp. 171-176
Author(s):  
Ilya M. Sobol ◽  
Boris V. Shukhman
Keyword(s):  
Monte Carlo ◽  
Error Estimate ◽  
Numerical Experiments ◽  
Probable Error ◽  
Quasi Monte Carlo ◽  
Integration Error ◽  
Asymptotic Error ◽  
Dimensional Cube ◽  
Integration Errors ◽  
Mc Method

AbstractA crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier {1/N}. However, the multiplier {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with {N=2^{m}} with natural m makes the integration error approximately proportional to {1/N}. In our numerical experiments, {d\leq 15}, and we used {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, {d\leq 2^{14}} and {N\leq 2^{63}}.

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