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 sun which is all energy sources, in today's society, hot water is used for various purposes starting from household to power production. People are adopting various ways to accomplish these goals, such as firewood heat and electrical power, so solar energy is an alternative to the dwindling resources of fossil fuels. Conversion of solar radiation into heat is one of the simplest and most direct applications of this energy, it can be used to heat water systems. A widely used flat-plate solar collector. In this study we have come to heat water using solar energy. This research presents the design and experimental analysis for using Spiral Flow Solar Water Heater (SFSWH) to enhance the thermal efficiency of a flat plate solar collector.
... Show MoreNumerical simulations are carried out to evaluate the coherence concept’s effect on the performance regarding the optical system, when observing and imaging the planet’s surface. In numerous optical approaches, the coherence qualities of light sources play an important role. This paper provides an overview about the mathematical formulation of temporal and spatial coherence and incoherence properties of light sources. The circular aperture was used to describe the optical system like a telescope. The simulation results show that diffraction-limited for incoherent imaging system certainly improves the image. Yet, the quality of the image is degraded by the light source's highly spatial and temporal coherence properties, resulting in a
... Show MoreThe great progress in information and communication technology has led to a huge increase in data available. Traditional systems can't keep up with this growth and can't handle this huge amount of data. Recommendation systems are one of the most important areas of research right now because they help people make decisions and find what they want among all this data. This study looked at the research trends published in Google Scholar within the period 2018-2022 related to recommending, reviewing, analysing, and comparing ebooks research papers. At first, the research papers were collected and classified based on the recommendation model used, the year of publication, and then they were compared in terms of techniques, datasets u
... Show MoreThrough the history of art movements, abstraction has been rotating between appearance and disappearance, mounting and stillness while its performances differed between reduction and simplification on the one hand and between the use of chromatographic and linear abstraction on the other. As a result, to what is mentioned, abstraction has appeared in many different artistic forms underlying the systematicity of the plastic art history.However, according to a contemporary point of view that comes up with the scientific revolution, the art of optical deceiving (illusion) appeared to find a hybrid art form that locates between the geometricity of abstraction and the scientific, visual and psychological foundations that are linked with the i
... Show MoreThe research focused on (balanced performance and structural mechanisms in industrial product design systems) by focusing on product development in a manner that is able to meet the human requirements through the effect of smart technology on the systems of product designs and its effectiveness in achieving the design and functional variables that have an effective effect in User and industrial products, correspond to the requirements of the user life at the level of daily interaction. The first chapter ensures the problem of research is the following question: What are the mechanisms to achieve balanced performance in some systems design to fit with the variables B N User and industrial products? The objective of the research was to ide
... Show MorePerhaps going to watch movies in cinemas today has become different from what it was before. The cinematic film, the clarity of the image and the luster of its colors pulled the rug out from under the most important change that occurred in the structure of the contemporary cinematography, which is the sound. The surround sound environment that immerses viewers in the realism of sound that reaches them from all directions, and for this the researcher found it necessary to shed light on this topic because of its importance, so the research problem was represented in the following question: (How are modern sound systems used in the structure of contemporary feature films?) The theoretical framework included two topics: the first: the dialec
... Show MoreFUZZY CONTROLLERS F'OR SINGLE POINT CONTROLLER-I (SPC-l) SYSTEMS
<p>The popularity, great influence and huge importance made wireless indoor localization has a unique touch, as well its wide successful on positioning and tracking systems for both human and assists also contributing to take the lead from outdoor systems in the scope of the recent research works. In this work, we will attempt to provide a survey of the existing indoor positioning solutions and attempt to classify different its techniques and systems. Five typical location predication approaches (triangulation, fingerprinting, proximity, vision analysis and trilateration) are considered here in order to analysis and provide the reader a review of the recent advances in wireless indoor localization techniques and systems to hav
... Show MoreEntrepreneurship, from a few years ago, is considered as a determining factor of the economic performances in the countries sending development. Its structural role and the dynamism it impels in all economies is no more established. For this reason, in this paper we proposed to use a methodology based on entrepreneurial and information systems for management master students in Ibn Zohr University Morocco. This methodology permit to facilitate to create the proper project in different disciplinary fields.
Nowadays, all agents insist on the development of entrepreneurship as well as the creation of enterprises as a catalyst for global economic growth. In this spirit, the development of the culture of business creation among students is
The main focus of this research is to examine the Travelling Salesman Problem (TSP) and the methods used to solve this problem where this problem is considered as one of the combinatorial optimization problems which met wide publicity and attention from the researches for to it's simple formulation and important applications and engagement to the rest of combinatorial problems , which is based on finding the optimal path through known number of cities where the salesman visits each city only once before returning to the city of departure n this research , the benefits of( FMOLP) algorithm is employed as one of the best methods to solve the (TSP) problem and the application of the algorithm in conjun
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