On the error term of the filon quadrature formulae

1987 ◽  
Vol 27 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Ulf Torsten Ehrenmark
Author(s):  
Gradimir Milovanovic

Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D. S. Mitrinovic, who left us 25 years ago. His significant inuence to the development of the theory of inequalities is briefly given in the first section of this paper. Beside some basic facts on quadrature formulas and an approach for estimating the error term using Ostrowski type inequalities and Peano kernel techniques, we give several examples of selected quadrature formulas and the corresponding inequalities, including the basic Ostrowski's inequality (1938), inequality of Milovanovic and Pecaric (1976) and its modifications, inequality of Dragomir, Cerone and Roumeliotis (2000), symmetric inequality of Guessab and Schmeisser (2002) and asymmetric in-equality of Franjic (2009), as well as four point symmetric inequalites by Alomari (2012) and a variant with double internal nodes given by Liu and Park (2017).


2007 ◽  
Vol 48 (4) ◽  
pp. 567-581 ◽  
Author(s):  
Gradimir V. Milovanović ◽  
Miodrag M. Spalević

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.


2020 ◽  
pp. 016327872098559
Author(s):  
Michael T. McKay ◽  
Frank C. Worrell ◽  
Jon C. Cole

The Adolescent and Adult Time Inventory–Time Attitudes Scale (AATI-TA) measures emotional engagement with the past, present, and future, and scores have been shown to relate meaningfully to health outcomes. For past, present, and future, five items are used to assess both positive and negative attitudes. Although evidence for the hypothesized six-factor solution has been widely reported, some studies have indicated problems with the Future Negative items. Given that a large and growing literature has emerged on the six-factor AATI-TA, and that AATI-TA scores have shown much better and more consistent fit than other temporal psychology measures, we sought to investigate the future negative factor in detail. Secondary analyses were performed on two datasets. The first was a University convenience sample ( N = 410) and the second was an adolescent sample ( N = 1,612). Confirmatory factor analyses revealed that the fit for the five Future Negative items was poor. Modification indices suggested that a correlated error term between Items 4 and 10 would result in good fit, and this was indeed the case. Models without Item 4 or Item 10 also yielded acceptable fit. Analyses using all four operationalizations of Future Negative (original scale, without Item 4 or Item 10, or with the correlated error between Items 4 and 10) to predict symptoms of anxiety and depression, and emotional self-efficacy revealed minor differences in the predictive validity coefficients. Potential ways forward, including a correlated error term or the dropping or replacement of Item 10, are discussed.


Sign in / Sign up

Export Citation Format

Share Document