|Article title||SOLUTION OF SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS BY THE METHOD OF SUMMATION OF DIVERGENT SERIES|
|Authors||V.V. Selyankin, V.I. Shmoylov|
|Section||SECTION II. MODELING OF COMPLEX SYSTEMS|
|Month, Year||06, 2015 @en|
|Abstract||Provides a method for solving systems of linear algebraic equations, which is based on the summation of the corresponding continued fractions. The resulting algorithm simple iteration approximation xi(0), xi(1), xi(2),..., xi(k) shall be considered as partial sums that converges if the iterative process converges and diverges - otherwise. For these partial sums constructed series, the first element of which pi(0) will coincide with хi(0), and subsequent members of the series pi(k) are difference xi(k)-xi(k-1). A number of construction, or associated with this next iteration process may converge slowly or even diverge. The summation of these series generated simple iteration algorithm, implemented the correct C-fractions, and constructed by series regular C-fractions are finite. Thus, the proposed algorithm for solving linear algebraic equation is classified as direct algorithms providing an exact solution of a finite number of operations. For exact solutions of linear algebraic equation is necessary to use the results of 2n iterations, where n - the dimension of the linear algebraic equation. At the same time, the proposed algorithm can provide and approximate solutions of system of linear equations when the number of iterations N<<2n, so we consider the algorithm as an iterative, with the high rate of convergence. Examples of solutions SLAE and evaluated the effectiveness of the algorithm.|
|Keywords||Acceleration of the convergence of iterative algorithms; continued fractions; and the summation of divergent series; exact methods SLAE|
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