Multigrid Method For Operator Equations Of The First Kind

This thesis is to present and analyze one class of Regularized Multi-grid Algorithms(RMGA) for solving operator equations of the first kind . The RMGA employs Tikhonov's Regularization to solve the corase grids equations with a new choicing parameter's posteriori-method for improving the numerical stability, and adopts a new smoothing strategy to correct the solutions on the fine grids for preserving the high efficiency of MGM.Meanwhile, some key technical problems in the process of implementation of RMGA are disscussed. The algorithm analysis and numerical tests have shown that the algorithm proposed in this paper is stable and highly effective, which provides a new useful tool for solving the operator equations of the first kind.