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 79
- Downloads 0
Identification of distribution features of the instantaneous power components of the electric energy of the circuit with polyharmonic current
Many researchers pay attention to the problem of the distortion electric power. The known theoretical results that are reflected in the acting standards are reasonably criticized in the part of the distortion power gener...
Development of a model of the weight of motor roads parameters as part of the information and management system of monetary evaluation
<p>The article deals with the approaches to the construction of a multi-level hierarchical system of indicators for evaluation of the quality state of a motor road section. The model of the weight of parameters and chara...
Estimation of the effect of temperature, the concentration of oxygen and catalysts on the oxidation of the thermoanthracite carbon material
<p>The effect of temperature, oxygen concentration and gas-air mixture flow rate on the oxidation efficiency of thermoanthracite carbon granular material with the formation of carbon monoxide and dioxide is considered. T...
Development of a decisionmaking method to form the indicators for a university development plan
<p>The problems of decision-making support in the course of designing a university development plan have been studied. This is important because modern tendencies in the development of higher educational institution are...
A study of multilayered electrochromic platings based on nickel and cobalt hydroxides
The multilayered electrochromic films based on Ni(OH)<sub>2</sub> and Co(OH)<sub>2</sub> have been prepared using sequential cathodic template deposition for solutions containing polyvinyl alcohol, nickel nitrate and cob...