The paper establishes explicit representations of the errors and residuals of approximate
solutions of triangular linear systems by Jordan elimination and of general linear algebraic
systems by Gauss-Jordan elimination as functions of the data perturbations and the rounding
errors in arithmetic floating-point operations. From these representations strict optimal
componentwise error and residual bounds are derived. Further, stability estimates for the
solutions are discussed. The error bounds for the solutions of triangular linear systems are
compared to the optimal error bounds for the solutions by back substitution and by Gaussian
elimination with back substitution, respectively. The results confirm in a very detailed form
that the errors of the solutions by Jordan elimination and by Gauss-Jordan elimination cannot
be essentially greater than the possible maximal errors of the solutions by back substitution
and by Gaussian elimination, respectively. Finally, the theoretical results are illustrated by
two numerical examples.
The current study is concerned with the analysis of spatial and temporal to death the elderly population in the city of Baghdad and at the level of administrative units Minor (districts and the areas) depending on the general population census of the province of Baghdad, data for 1997 and data from the Ministry of Health Department of Health and Vital Statistics for 2013.
The study showed differing age and quality of mortality rates at the level of administrative units of the study area, and notes the high mortality rates of elderly people of all age groups in 2013 compared to 1997, and this is due to security conditions after the USA occupation, and the accompanying conditions have affected the increase in mortality rates.
The research aims to measure the sustainability of the Iraqi economy for the period 1990-2018 as well as to show the impact of fluctuations in the level of GDP on financial sustainability, where financial sustainability is the necessary and sufficient condition for achieving economic and financial balance in the country, as financial sustainability reflects the movement of the state budget and its relationship to GDP through the indicators of deficit, fiscal surplus and public debt internal and external, as well as reflecting the art of managing public debt, and the more managed public debt is achieved, the more the management of public debt is achieved financial sustainability. for the state in the sense that there is a reciprocal
... Show MoreMedical images play a crucial role in the classification of various diseases and conditions. One of the imaging modalities is X-rays which provide valuable visual information that helps in the identification and characterization of various medical conditions. Chest radiograph (CXR) images have long been used to examine and monitor numerous lung disorders, such as tuberculosis, pneumonia, atelectasis, and hernia. COVID-19 detection can be accomplished using CXR images as well. COVID-19, a virus that causes infections in the lungs and the airways of the upper respiratory tract, was first discovered in 2019 in Wuhan Province, China, and has since been thought to cause substantial airway damage, badly impacting the lungs of affected persons.
... Show MoreThe parametric programming considered as type of sensitivity analysis. In this research concerning to study the effect of the variations on linear programming model (objective function coefficients and right hand side) on the optimal solution. To determine the parameter (θ) value (-5≤ θ ≤5).Whereas the result، the objective function equal zero and the decision variables are non basic، when the parameter (θ = -5).The objective function value increases when the parameter (θ= 5) and the decision variables are basic، with the except of X24, X34.Whenever the parameter value increase, the objectiv
... Show MoreWith the spread of the use of liquefied petroleum gas (LPG) in developing countries for use in domestic cooking with the increase in the expansion and distribution of gas pipelines for residential buildings, the 2002 World Summit focused on sustainable development in clean energy for natural gas (NG) and LPG. The research aims to focus on the important aspects of design sustainability from an environmental point of view to reduce gas leakage, accidents, and explosions that occur socially to expand the distribution of LPG and motivate the consumers to use it instead of natural gas and other fuels, and from an economic point of view to take into account the annual cost and aesthetic imp
Stylistics represents a modern approach in understanding the literary text through the linguistic patterns that form it. The distinctive phenomena that the text includes constitute special features in it. As well as exploring its aesthetic aspects through description and analysis at the same time. The close link between stylistics and linguistics made stylistics occupy a prominent place in modern literary criticism.
In this regard, we do not want to dwell on the different directions of stylistics. Rather, we will prolong the discussion in the study of the style as a (deviation. Aversion) from the original. Because this trend plays on the chord of the paradox between the surface structure and the deep structure, especially when the sur