The restarted generalized minimal residual (denoted as GMRES(m)) normally used for solving a linear system of equations of the form Ax=b has the drawback of eventually presenting a stagnation or a slowdown in its rate of convergence at certain restarting cycles. In this article, a switching controller is introduced to modify the structure of the GMRES(m) when a stagnation is detected, enlarging and enriching the subspace. In addition, an adaptive control law is introduced to update the restarting parameter to modify the dimension of the Krylov subspace. This combination of strategies is competitive from the point of view of helping to avoid the stagnation and accelerating the convergence with respect to the number of iterations and the computational time. Computational experiments corroborate the theoretical results.

中文翻译：

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使用自适应开关控制器改善GMRES（m）

通常用于求解形式为Ax = b的线性方程组的重新启动的广义最小残差（表示为GMRES（m））具有在某些重新启动周期中最终呈现出停滞或收敛速度变慢的缺点。本文介绍了一种开关控制器，用于修改GMRES（m），当检测到停滞时，扩大并丰富了子空间。另外，引入了自适应控制定律以更新重启参数以修改Krylov子空间的维数。从帮助避免停滞并加快迭代次数和计算时间的收敛角度来看，这种策略组合具有竞争力。计算实验证实了理论结果。