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。我们探讨了不同的正则化方法，作为一种手段，产生稳定的解决方案的线性离散不适定问题。与GMRES正则化必须实现在两个阶段，这是设计来产生一个近似的解决方案的线性系统，通过使用GMRES，并确定最合适的解决方案，通过使用一个约束。在第一阶段中，特定的行为GMRES和预处理GMRES线性离散不适定问题。在第二阶段，一个简化的Tikhonov阈值作为约束条件，以确定最佳的近似解进行了探索。数值实验已制成表格，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.