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.
Information and Communication Technology revolution has led to the emergence of electronic payment systems and their means And that the replacement of these modern means replace the traditional means (legal money) issued by the Central Bank has influenced the performance of monetary policy, especially that monetary policy is one of the most important policies used to achieve economic stability , The aim of the research is To know the impact of electronic payment systems on the tools of monetary policy as these means, such as cards and electronic money issued by credit institutions and companies, that is, the Central Bank is not responsible for issuance and spread And the lack of regulation by the Central Bank will lea
... Show MoreA theoretical study has been proposed to investigate the effects of different laser radiations (Nd - glass, DF and C02) as a heating source on different glass samples (Optical glass, Bk - 7 and Soda - lime glass) and different waves lengths (10.6, 3.8, 1.6) ???. The heat changes as which are resulted due irradiation with laser sources have been determined by using the one dimension mathematical relation as a function of time (t) and depth (z). The results of the study show ed that the irradiation with C02 laser had a greater effect than DF laser, while the effects of Nd - glass laser were minimal with a power density of (1.8*10?? w/m2) within atime(l^sec).(Forboth Kinds) The change in the temperatures were not exceeded than (70"K) in all sa
... Show MoreWater is necessary for sustainable development and healthy society. Groundwater, often, is not sufficient and protected for direct human consumption. Due to increase in the density of population the requirement of water is increasing. In this work, the assessment of groundwater quality was conducted in the south-west part of Basrah province. Spatial variations in the quality of groundwater in the study area have been analyzed utilizing GIS technique. The geochemical parameters of groundwater samples including pH, EC, TDS, Ca, Mg, Na, Cl, HCO3, SO4, and NO3 were assessed in this study. Information maps of the study area have been actually prepared to make use of the GIS spatial
... Show MoreThis study was conducted to study the cytogenetic effect of both alcoholic and water extracts of propolis on mice. Three different samples of propolis were collected from three different regions of Iraq (Najaf, Arbil and Baghdad) to be used in this study. The cytotoxic effect of two different doses of each extracted sample was measured by employing cytogenetic analysis which included (mitotic index (MI), chromosomal aberrations (CAs), micronucleus index (MN) and sperm abnormalities). Results showed that significant increase in MI and significant reduction in MN, CAs and sperm abnormalities percentage were seen after treatment with both alcoholic and water extract of the three samples when compared with negative control, and alcoholic extrac
... Show MoreA Raman spectroscopy method was optimised to examine the chemical changes of aspirin tablets after interaction with helium temperatures. Several aspirin tablets were exposed to plasma-assisted desorption ionisation flame for different times (10, 30, 50, 60, 180 and 300s) and then analysed by Raman spectroscopy using optimal conditions. The changes in chemistry between exposed and fresh (without exposure to plasma) tablets were compared. The vibrational peaks of the aspirin molecule in the Raman spectrum were identified by checking the peak position. The results showed clear spectra with increases in intensity of vibrational peaks until 30s, whereas no spectra were measured for the exposed tablets to plasma flame after 50s. It can, the
... Show MoreThe purpose of current study is to analyze the computer textbooks content for intermediate stage in Iraq according to the theory of multiple intelligence. By answering the following question “what is the percentage of availability of multiple intelligence in the content of the computer textbooks on intermediate stage (grade I, II) for the academic year (2017-2018)? The researcher followed the descriptive analytical research approach (content analysis), and adopted an explicit idea for registration. The research tool was prepared according the Gardner’s classification of multiple intelligence. It has proven validity and reliability. The study found the percentage of multiple intelligence in the content of computer textbooks for the in
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