# American Institute of Mathematical Sciences

May  2019, 2(2): 83-93. doi: 10.3934/mfc.2019007

## "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

 1 Stevana Mokranjca 6, 12000 Požarevac, Serbia 2 Visoka Tehnička škola strukovnih studija, Njegoseva 2, 12000 Požarevac, Serbia

* Corresponding author: Aleksa Srdanov

Received  February 2019 Revised  March 2019 Published  May 2019

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.

Citation: Aleksa Srdanov, Radiša Stefanović, Aleksandra Janković, Dragan Milovanović. "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. Mathematical Foundations of Computing, 2019, 2 (2) : 83-93. doi: 10.3934/mfc.2019007
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##### References:
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