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Quasi-Chebyshev accelerated iteration methods based on optimization for linear systems

机译:基于线性系统优化的拟切比雪夫加速迭代方法

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In this paper, we present a quasi-Chebyshev accelerated iteration method for solving a system of linear equations. Compared with the Chebyshev semi-iterative method, the main difference is that the parameter ω is not obtained by a Chebyshev polynomial but by optimization models. We prove that the quasi-Chebyshev accelerated iteration method is unconditionally convergent if the original iteration method is convergent, and also discuss the convergence rate. Finally, three numerical examples indicate that our method is more efficient than the Chebyshev semi-iterative method.
机译:在本文中,我们提出了一种用于求解线性方程组的拟Chebyshev加速迭代方法。与Chebyshev半迭代法相比,主要区别在于参数ω不是通过Chebyshev多项式获得的,而是通过优化模型获得的。我们证明了如果原始迭代方法是收敛的拟切比雪夫加速迭代方法是无条件收敛的,并讨论了收敛速度。最后,三个数值示例表明我们的方法比Chebyshev半迭代方法更有效。

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