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The method of 'external spiral" for solving a large system of linear equations

Journal: VOJNOTEHNICKI GLASNIK / MILITARY TECHNICAL COURIER (Vol.66, No. 2)

Publication Date:

Authors : ; ; ; ; ;

Page : 399-414

Keywords : system of linear equations; method of 'external spiral"; hyperplane;

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Abstract

Solving a linear system of n × n equations can be very difficult for the computer, especially if one needs the exact solution, even when the number n - of equations and of unknown variables is relatively small (a few thousands). All existing methods have to overcome at least one of the following problems: 1. Computational complexity, which is expressed with the number of arithmetic operations required in order to determine a solution; 2. The possibility of overflow and underflow problems; 3. Causing variations in the values of some coefficients in the initial system, which may be leading to instability of the solution; 4. Requiring additional conditions for convergence; 5. In cases of a large number of equations and unknown variables it is often required that the systems matrix be: either sparse, or symmetrical, or diagonal, etc. This paper presents a method for solving a system of linear equations of arbitrary order (any number of equations and unknown variables) to which the problems listed above do not reflect.

Last modified: 2018-04-24 17:37:31