Search results for "approximation error"
showing 10 items of 62 documents
Quantitative approximation of certain stochastic integrals
2002
We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably.
Influence of pixel size on quantification of airway wall thickness in computed tomography.
2009
Objectives: The purpose of this study was to determine the point where a further decrease in voxel size does not result in better automatic quantification of the bronchial wall thickness by using 2 different assessment techniques. Materials and Methods: The results from the commonly used full-width-at-half-maximum (FWHM) principle and a new technique (integral-based method [IBM]) were compared for thin-section multidetector computed tomography (MDCT) data sets from an airway phantom containing 10 different tubular airway phantoms and in a human subsegmental bronchus in vivo. Correlation with the actual wall thickness and comparison of the wall thicknesses assessed for different voxel sizes …
Finite element approximation of vector fields given by curl and divergence
1981
In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested.
On the finite element approximation for maxwell’s problem in polynomial domains of the plane
1981
The time-harmonic Maxwell boundary value problem in polygonal domains of R2 is considered. The behaviour of the solution in the neighbourhood of nonregular boundary points is given and asymptotic error estimates in L2- and in curl-div-norm for a finite element approximation of the solution are derived
Influence of the porosity profile and sets of Ergun constants on the main hydrodynamic parameters in the trickle-bed reactors
2014
Abstract The Eulerian multiphase code has been applied for the comparative simulation of the experimental results obtained for varying flow rates of both fluid phases and for systems of various physicochemical properties used in the laboratory trickle-bed reactor (TBR). Therefore six different radial porosity profiles and three sets of the Ergun constants used in the relations defining the interphase momentum exchange have been implemented into the CFD code. The mean relative error of the pressure drop and of the averaged holdup as well as the standard deviation determined with respect to the experiments have been used as the criterion for the validation of the theoretical model. These valu…
Chromatographic multivariate quality control of pharmaceuticals giving strongly overlapped peaks based on the chromatogram profile
2004
In the present paper, the simultaneous quantification of two analytes showing strongly overlapped chromatographic peaks (alpha = 1.02), under the assumption that both available equipment and training of the laboratory staff are basic, is studied. A pharmaceutical preparation (Mutabase) containing two drugs of similar physicochemical properties (amitriptyline and perphenazine) is selected as case of study. The assays are carried out under realistic working conditions (i.e. routine testing laboratories). Uncertainty considerations are introduced in the study. A partial least squares model is directly applied to the chromatographic data (with no previous signal transformation) to perform quali…
Mass and energy flux estimates at different spatial resolutions in a heterogeneous area through a distributed energy-water balance model and remote s…
2012
Computed ET with the FEST-EWB model at high spatial resolution 10 m showed for the three days of analysis a mean relative error of 9.4% compared to AHS data, whereas for land surface temperature comparison a relative error of 1.6% was found. Then, LSTs from AHS and FEST-EWB were aggregated at decreasing spatial resolutions 50, 150, 300, 400, 500, 600, 750, and 1000 m, showing that the thermodynamic variability tends to disappear with a lower number of classes in the histograms and with a decrease of the coefficient of variation CV and of standard deviation values. At each scale, a similar behaviour was reported between each pair of images, with the values of standard deviation starting, res…
Proximal-sensing-powered modelling of energy-water fluxes in a vineyard: A spatial resolution analysis
2021
Spatial resolution is a key parameter in energy–water surface flux modelling. In this research, scale effects are analyzed on fluxes modelled with the FEST-EWB model, by upscaling both its inputs and outputs separately. The main questions are: (a) if high-resolution remote sensing images are necessary to accurately model a heterogeneous area; and (b) whether and to what extent low-resolution modelling provides worse/better results than the upscaled results of high-resolution modelling. The study area is an experimental vineyard field where proximal sensing images were obtained by an airborne platform and verification fluxes were measured via a flux tower. Modelled fluxes are in line with th…
Description of x-ray beams using the fluorescence yields of a set of thick targets
1995
Quantitative methods in x-ray fluorescence analysis require a knowledge of the spectral distribution of the fluorescence-exciting beam. The use of XRF yield measurements of a set of thick pure element targets is proposed for the description of a fluorescence-exciting x-ray beam, without the need to obtain its spectral distribution. This new approach is derived theoretically and verified by comparing thin-target yields calculated from XRF yield measurements of thick pure element specimens with those obtained from a calculated spectral distribution. The difference between the two methods of obtaining the thin-target yields is within 9% relative error.
On the use of asymptotic expansion in computing the null distribution of page's L-statistic
1989
Suppose that each out of n randomized complete blocks is obtained by observing a jointly continuous random variable taking values in Rk. Page's L-statistic is given then as a sum of i.i.d. lattice variables with finite moments of any order. Applying a well-known theorem on asymptotic expansions for the distribution function of such a sum yields higher order approximations to the significance probability of any observed value of L. The formula obtained by discarding terms smaller than o(n –1) is still very simple to use. Yet, due to it's strong analytical basis, it can be expected to provide substantial improvement on the traditional normal approximation. The results of extensive numerical i…