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"Reducing the number of dimensions of the possible solution space" as a method for finding the exact solution of a system with a large number of unknowns

  • * Corresponding author: Aleksa Srdanov

    * Corresponding author: Aleksa Srdanov 
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  • Solving linear systems with a relatively large number of equationsand unknowns can be achieved using an approximate method to obtain a solution with specified accuracy within numerical mathematics. Obtaining theexact solution using the computer today is only possible within the frameworkof symbolic mathematics. It is possible to define an algorithm that does notsolve the system of equations in the usual mathematical way, but still findsits exact solution in the exact number of steps already defined. The methodconsists of simple computations that are not cumulative. At the same time,the number of operations is acceptable even for a relatively large number ofequations and unknowns. In addition, the algorithm allows the process to startfrom an arbitrary initial n-tuple and always leads to the exact solution if itexists.

    Mathematics Subject Classification: Primary: 15A06; Secondary: 65F99.


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    [3] D. A. Randall, An Introduction to Numerical Modeling of the Atmosphere, 2015, Chapter 6, Colorado State Univesity.
    [4] A. Srdanov, The universal formulas for the number of partitions, Proc. Indian Acad. Sci. Math. Sci., 128 (2018), Art. 40, 17 pp. doi: 10.1007/s12044-018-0418-z.
    [5] A. Srdanov and R. Stefanović, How to solve a system of linear equations with extremely many unknown, (Serbian), 16th International Symposium INFOTEH-Jahorina, 16 (2017), 593–596, Available from: https://www.infoteh.rs.ba/zbornik/2017/radovi/RSS-2/RSS-2-12.pdf
    [6] A. SrdanovR. StefanovićN. Ratković KovačevićA. Jovanović and D. Milovanović, The method of external spiral for solving large system of linear equations, Military Technical Courier, 66 (2018), 391-414.  doi: 10.5937/vojtehg66-14625.
    [7] A. Srdanov, R. Stefanović, N. Ratković Kovačević, A. Jovanović, D. Milovanović and D. Marjanović, Method of trihedrals for finding the exact solution of a linear system with a large number of unknowns, (Serbian), 17th International Symposium INFOTEH-Jahorina, (2018), 388–392, Available from: https://www.infoteh.rs.ba/zbornik/2018/radovi/RSS-3/RSS-3-1.pdf
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