Randomized vector iterative linear solvers of high precision for large dense system

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2023-10-04 DOI:10.1515/mcma-2023-2013
Karl K. Sabelfeld, Anastasiya Kireeva
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Abstract

Abstract In this paper we suggest randomized linear solvers with a focus on refinement issue to achieve a high precision while maintaining all the advantages of the Monte Carlo method for solving systems of large dimension with dense matrices. It is shown that each iterative refinement step reduces the error by one order of magnitude. The crucial point of the suggested method is, in contrast to the standard Monte Carlo method, that the randomized vector algorithm computes the entire solution column at once, rather than a single component. This makes it possible to efficiently construct the iterative refinement method. We apply the developed method for solving a system of elasticity equations.
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大型密集系统高精度随机向量迭代线性求解器
在本文中,我们提出了随机线性求解器,重点是细化问题,以实现高精度,同时保持蒙特卡罗方法在求解具有密集矩阵的大维系统时的所有优点。结果表明,每个迭代细化步骤减小误差的数量级。与标准蒙特卡罗方法相比,所建议的方法的关键点是随机向量算法一次计算整个解列,而不是单个分量。这使得有效地构造迭代细化方法成为可能。我们应用所开发的方法来求解弹性方程组。
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来源期刊
Monte Carlo Methods and Applications
Monte Carlo Methods and Applications STATISTICS & PROBABILITY-
CiteScore
1.20
自引率
22.20%
发文量
31
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