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

GMRES 正则化方法可以说是线性离散不适定问题最流行的解决方案。我们探索了不同的正则化方法，作为产生线性离散不适定问题的稳定解的手段。GMRES 正则化必须分两个阶段实施，旨在通过使用 GMRES 生成线性系统的近似解，并通过使用约束来确定最合适的解。在第一阶段，确定了 GMRES 和针对线性离散不适定问题的预处理 GMRES 的特定行为。在第二阶段，探索简化的吉洪诺夫阈值作为确定最佳近似解的约束。数值实验已制成表格，以强调我们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.