【作者】 赵振宇；

【导师】 肖庭延；

【作者基本信息】 河北工业大学 ， 应用数学， 2004， 硕士

【摘要】 本文将提出一类适合第一类算子方程的正则化的多重网格算法，它结合一种新的正则参数选取准则，应用Tikhonov正则化来求解粗网格方程保证了求解的稳定性；而在将解向细网格延拓时使用了一种新的光顺处理策略。文中还对实施算法的若干技术问题进行了讨论。数值实验结果表明本文提出的算法是稳定高效的，为第一类算子方程的求解提供了一个新的有效工具。更多还原

【Abstract】 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.更多还原