scholarly journals Two-point formulae of Euler type

2002 ◽  
Vol 44 (2) ◽  
pp. 221-245 ◽  
Author(s):  
M. Matić ◽  
C. E. M. Pearce ◽  
J. Pečarić
Keyword(s):  
Error Estimates ◽  
Bounded Variation

AbstractAn analysis is made of quadrature viatwo-point formulae when the integrand is Lipschitz or of bounded variation. The error estimates are shown to be as good as those found in recent studies using Simpson (three-point) formulae.

ON A GENERALISED TRAPEZOIDAL RULE FOR FUNCTIONS OF BOUNDED VARIATION

2009 ◽  
Vol 02 (02) ◽  
pp. 191-200
Author(s):  
P. Cerone ◽  
S. S. Dragomir ◽  
A. McAndrew
Keyword(s):  
Error Estimates ◽  
Bounded Variation ◽  
Trapezoidal Rule ◽  
Functions Of Bounded Variation

A generalised trapezoidal rule is considered. Error estimates for functions of bounded variation are given. Applications for some particular cases of interest are provided as well.

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 Generalisation of a corrected Simpson's formula

2006 ◽  
Vol 47 (3) ◽  
pp. 367-385 ◽  
Author(s):  
J. Pečarić ◽  
I. Franjić
Keyword(s):  
Error Estimates ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Lipschitzian Functions ◽  
Integrable Functions

AbstractThe results obtained by A. J. Roberts and N. Ujević in a recent paper are generalised. A number of inequalities for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or R-integrable functions are derived. Also, some error estimates for the derived formulae are obtained.

Systematic effects in observed parallaxes

1978 ◽  
Vol 48 ◽  
pp. 31-35
Author(s):  
R. B. Hanson
Keyword(s):  
Error Estimates ◽  
Zero Point ◽  
Absolute Zero ◽  
Apparent Magnitude ◽  
Coherent System ◽  
Preliminary Results ◽  
General Catalogue ◽  
Systematic Effects ◽  
New Evidence ◽  
Right Ascension

Several outstanding problems affecting the existing parallaxes should be resolved to form a coherent system for the new General Catalogue proposed by van Altena, as well as to improve luminosity calibrations and other parallax applications. Lutz has reviewed several of these problems, such as: (A) systematic differences between observatories, (B) external error estimates, (C) the absolute zero point, and (D) systematic observational effects (in right ascension, declination, apparent magnitude, etc.). Here we explore the use of cluster and spectroscopic parallaxes, and the distributions of observed parallaxes, to bring new evidence to bear on these classic problems. Several preliminary results have been obtained.

Sign in / Sign up

Export Citation Format

Share Document