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Superfast Iterative Solvers for Linear Matrix Equations

Е. А. Микрин, Nikolay E. Zubov, D. E. Efanov, Vladimir Nikolaevich Ryabchenko

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Abstract

Superfast algorithms for solving large systems of linear equations are developed on the basis of an original method for multistep decomposition of a linear multidimensional dynamical system. Examples of analytical synthesis of iterative solvers for matrices of the general form and for large numerical systems of linear algebraic equations are given. For the analytical case, it is shown that convergence occurs at the second iteration.

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What this paper is about

Superfast algorithms for solving large systems of linear equations are developed on the basis of an original method for multistep decomposition of a linear multidimensional dynamical system. Examples of analytical synthesis of iterative solvers for matrices of the general form and for large numerical systems of linear algebraic equations are given. For the analytical case, it is shown that convergence occurs at the second iteration.

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OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Superfast algorithms for solving large systems of linear equations are developed on the basis of an original method for multistep decomposition of a linear multidimensional dynamical system. Examples of analytical synthesis of iterative solvers for matrices of the general form and for large numerical systems of linear algebraic equations are given. For the analytical case, it is shown that convergence occurs at the second iteration.

Key concepts: Mathematics, Algebraic equation, Linear system, Iterative method, System of linear equations, Applied mathematics, Convergence (economics), Linear equation

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