Advancement of a long arithmetic technology in the construction of algorithms for studying linear systems
Journal Title: Восточно-Европейский журнал передовых технологий - Year 2019, Vol 1, Issue 4
Abstract
<p>We have advanced the application of algorithms within a method of basic matrices, which are equipped with the technology of long arithmetic to improve the precision of performing the basic operations in the course of studying the ill-conditioned linear systems, specifically, the systems of linear algebraic equations (SLAE). Identification of the fact of ill-conditionality of a system is a rather time-consuming computational procedure. The possibility to control computations entering the state of incorrectness and the impossibility of accumulating calculation errors, which is a desirable property of the methods and algorithms for solving practical problems, were introduced.</p>Modern computers typically use the standard types of integers whose size does not exceed 64 bytes. This hardware limitation was resolved using software, specifically, by developing a proprietary type of data in the form of a special Longnum library in the C++ language (using the STL (Standard Template Library)). Software implementation was aimed at carrying out computations for methods of basic matrices (MBM) and Gauss matrices, that is, long arithmetic for models with rational elements was used. We have proposed the algorithms and computer realization of the Gauss type methods and methods of artificial basic matrices (a variant of the method of basic matrices) in MatLAB environment and Visual C++ environment using precise computation of the methods' elements, first of all, for the ill-conditioned systems of varying dimensionality. The Longnum library with the types of long integers (longint3) and rational numbers (longrat3) with the numerator and denominator of the longint3 type was developed. Arithmetic operations on long integers were performed based on the modern methods, including the Strassen multiplication method. We give the results from the computational experiment employing the mentioned methods, in which test models of the systems were generated, specifically, based on the Gilbert matrices of different dimensionality
Authors and Affiliations
Volodymyr Kudin, Viacheslav Onotskyi, Ali Al-Ammouri, Lyudmyla Shkvarchuk
Keywords
Related Articles
- EP ID EP666177
- DOI 10.15587/1729-4061.2019.157521
- Views 76
- Downloads 0
Comparative tests of contact elements at current collectors in order to comprehensively assess their operational performance
<p>We have studied the interaction between contact elements in the pantographs of electric transport under operation at the sections of railroads powered by direct and alternating current. In contrast to known techniques...
Development of the method for the optimal management of occupational risks
<p>Within the framework of this research, we analyzed international normative and legal documents on risk management in the field of occupational health and safety and identified the following shortcomings:</p><p>– uncer...
Development of the ñonverter structure that enables power supply to traction induction motors of mine electric locomotives from different levels of voltage
<p class="a">We have proposed an adjustable structure of the converter of energy of electric drive in the electrotechnical complex of a mine electric locomotive from power sources with different voltage levels ‒ from a c...
Synthesis of energyefficient acceleration control law of automobile
<p>We have established the laws of change in the vehicle acceleration time at the existing step transmission of ICE, when implementing the total traction force, boundary for the drive wheels adhesion to the road, and dur...
Development of a criteriabased approach to agroecological assessment of slope agrolandscapes
<p class="a">For the forecast and management of erosion processes in order to protect the environment, information is needed on the state of its components and impact factors as well as the results of this impact. The ex...