Parallel Iterative Schemes of Linear Algebra with Application to the Stability Analysis of Solutions of Systems of Linear Differential Equations |
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Authors: | Ya. E. Romm |
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Affiliation: | (1) State Pedagogical Institute, Taganrog, Russia |
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Abstract: | Parallel modifications of linear iteration schemes are proposed that are used to solve systems of liner algebraic equations and to achieve the time complexity equal to T = log2k · O(log2n), where k is the number of iterations of an original scheme and n is the dimension of a system. Such schemes are extended to the case of approximate solution of systems of linear differential equations with constant coefficients. Based on them and using a program, the stability of solutions in the Lyapunov sense is analyzed. |
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Keywords: | parallel algorithm time complexity linear algebra linear differential equation stability |
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