New GMRES algorithm for solving large scale inverse problems on a cloud computing

GMRES正则化方法是求解线性离散病态问题最常用的方法。我们探索了不同的正则化方法作为线性离散病态问题稳定解的一种手段。GMRES的正则化必须分两个阶段实现，这两个阶段旨在通过使用GMRES生成线性系统的近似解，并通过使用约束确定最合适的解。首先对线性离散病态问题的GMRES和预条件GMRES的特殊行为进行了辨识；在第二阶段，研究了一个简化的Tikhonov阈值作为约束来确定最佳近似解。数值实验已被制成表格以强调我们所提出的方法的有效性。

GMRES regularization method is arguably the most popular solution for linear discrete ill-posed problems. We explores different regularization methods as a means of yielding stable solutions for linear discrete ill-posed problems.The regularization with GMRES must be implemented in two stages, which are designed to generate an approximate solution of a linear system through the use of GMRES, and to determine the most appropriate solution by using a constraint. In the first stage, particular behaviors of GMRES and preconditioned GMRES for linear discrete ill-posed problems are identified. In the second stage, a simplified Tikhonov threshold as a constraint to determine the best approximate solution is explored. Numerical experiments have been tabulated to underline the effectiveness of our proposed method.