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13l_J- the keyboard and a mouse work in a guest operating system.
The computer under control of Linux is loaded much more long, than under control of Windows. It also is the negative moment when using this system in educational process. But nevertheless, use of virtual computers and the Linux operating system allows pupils to understand better that fact that except Windows there are other operating systems. And here the knowledge of bases of the organization of operating systems and the principles of their functioning is not only desirable, but obligatory.
Uses in training of technologies of virtual computers while it is widespread a little. We consider that development of this subject can increase efficiency of teaching of information disciplines considerably.
REFERENCES
1. Усманов Ш.Н. Виртуальные машины в преподавании информатики. 2007. (Usmanov Sh. N. Virtual computers in informatics teaching.) http://www.rusedu.info/Article787.html
2. Леонов В. Секреты Linux. М.: Эксмо, (Leonov V. Linux secrets.) 2010. - 336 с.
3. Сушков С.А. «Новые подходы к обучению ИТ-дисциплинам будущих учителей информатики». (Sushkov S. A. "New approaches to training in IT disciplines of future teachers of informatics") 2007.
4. http://ru.wikipedia.org/wiki/virtualbox/
5. http://inflin.narod.ru/
THEORETICAL EVALUATING THE EFFECTIVENESS OF
THE ALGORITHM
Zhanys Aray Boshanqyzy PhD, professor
Professor Russian Academy of Natural number 7524 Kokshetau University named after Abay Myrzahmetova mobile: 8-701-217-80-82, email: aray.zhanys@gmail.com Republic of Kazakhstan, Kokshetau, 020000
Nurkasymova Saule Nurkasymovna doctor of pedagogical sciences, professor Eurasian National University by name is L.N. Gumilyov Republic of Kazakhstan, Astana, 010000 mobile: 87753694697SauleNurkasim@mail.ru
Nadyrova Fatima Kamalovna Lecturer, Department of Information and Computer Science ssitemy Kokshetau University named after Abay Myrzahmetova mobile: 8-701-217-80-82, email: aray.zhanys@gmail.com Republic of Kazakhstan, Kokshetau, 020000
Abstract. This paper describes the author developed an algorithm for obtaining expressions for the recording of the root system of linear algebraic equations analytically. We present a theoretical basis reduce the time for solving systems of equations by using this algorithm with dense matrices filled. It is shown that by using the proposed algorithm is applied to sparse systems of equations also manages to achieve an increase in the rate of production decisions, with even more reduced the cost of RAM.
Keywords: Efficiency, algorithm, system of linear equations, Gauss method, matrix, classic stimulant, a mathematical model, a stimulant, the number of iterations linearization, integration, information systems, inert process processing core.
Evaluating the effectiveness of the filled matrix.
According to [14, 15], complexity of algorithms for the forward and reverse strokes Gauss defined as 0(n3) for the direct flow of Gauss and 0(n2) to reverse the Gauss method for filling, not diluted, matrices.
Accordingly, the overall complexity of the mathematical model of a part of the classic simulation when using Gauss method as a method for solving linear systems can be represented as an expression of the form (1):
DCSLES = N,M • Nlm • (n3 + n2) , (1)
Dcsles -complexity of the mathematical models in conventional design simulation program, expressed in the number of mathematical operations of multiplication and division
NIM- the number of integration steps,
Nlm~ iterations linearization
n- dimension of the linear system of equations describing the mathematical model simulated information systems.
At the same time an expression for calculating the complexity of solving a mathematical model using the developed algorithm can be estimated by (2):
Dnsles = Dsym + N™ • Nlm • n2, (2)
In this expression, the following designations:
DN sles -complexity of the mathematical model in the proposed version of the program - a simulator, expressed in number of mathematical operations of multiplication and division,
DSYm~ difficulty of obtaining expressions for the roots of a system of linear algebraic equations in explicit form,
NIM- number of steps of the method of integration,
Nlm~ the number of iterations of the linearization method,
n- dimension of the system of linear algebraic equations describing the mathematical model that simulated information system.
In addition to the expected growth rate according to the expressions (1) and (2), the use of the algorithm for calculating the roots Slough also has significant advantages in the generation of code for multi-processor computing.
Evaluating the effectiveness of the application of the algorithm for solving systems of equations presented in the form of a sparse matrix.
Compared with the use of sparse matrices, application of this algorithm will yield significant cost reduction RAM.
Assuming that the matrix shown in Fig. 1, stores real numbers, the total amount of memory required to store the complete matrix is (assuming that the real number is 8 bytes) 8 * 5 * 5 = 200bayt.
The amount of memory required to store the same matrix using a sparse matrix storage format, is (provided that the real number 8bayt takes in memory, and an integer representing the elements of the vectors, JA, IA, 4bayta) 8 * 9 * 4 + 9 + 4 * 6 = 132bayta.
Application of the developed algorithm allows to take for storing elements of this matrix is only 8 * 9 = 72bayta RAM. If you operate with the terms format AIJ, in the memory of place is only the vector AN, vector values are not zero elements. For a given in the first chapter of optimized modeling of IP storage format, the memory is spent only for items DIA G and AN.
Fig. 2 shows the amount of memory for a variety of storage methods on the dimension of the system of equations. The data obtained on the assumption that with increasing dimensionality of the system of equations the mean number of elements connected to each of the nodes is equal to 4.
Decision as MM A$ + B = 0
Fig. 1. The modified process offorming a mathematical model.
Fig. 2. Otsenka cost of RAM.
Fig. 2-a shows the effectiveness of the methods of storing sparse matrices (graph 1) compared to the cost of memory for storage full matrix (Fig. 1)
Risunok 2- b to evaluate the difference in the cost of memory for storing sparse matrix methods: the method of storage format AIJ (graph 2) and the proposed algorithm (Fig. 3).
Analyzing the graphs, one can conclude the greater efficiency of memory usage in the case of using the proposed algorithm storage component matrices.
Evaluating the effectiveness of the application of the algorithm using the algorithm parallelization.
9 = F(Yij,...,Ykl,Im,...,In, 9^,..., 90) (3)
Expression (3) is written in the so-called "sensitive" form. The term "dependent form of the expression for calculating the roots" we understand such a record, using the following which each value of the root system of linear algebraic equations depend not only on the values of the elements of the matrix conductivities and vector currents, but also on the already calculated values of the root. This type of expression is observed in the calculation of the root system of linear algebraic uravneniipri implementation of the conventional method of Gauss. With this form of recording can not be calculated following the root, not having received the previous value.
Through the use of the compilation approach to the formation of mathematical models of IP, namely due to the fact that the code to retrieve the values of the root SLAE formed before it is used in the calculations, it is possible to expand an expression of the form (3.4) in order to express the desired values of the roots and the destination file with the source code Programs- simulator were only expressions of the form (4):
9 = F(Yj,...,Yki,Im,...,In) . (4)
The form of writing expressions for calculating the value of the root recorded in this form will be called "independent form of writing."
Obviously, such a record requires more time for its formation, as more time is spent on the deployment of elements of the root values. However, it is ideally suited for parallel computing. The values of the vector elements root SLAE recorded as (3) comprise mutually independent instructions for computing and hence can be computed independently, but on different computing nuclei.
REFERENCES
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2. Zhanys A. B., Nurkasymova S. N. Results of the Pedagogical Experiment for Determination of Forming of the basic Knowledge in Mathematics. Indian Journal of Science and Technology, Vol 8(13), 59959, July 2015
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