投影SOR迭代求解双边障碍问题

Projected SOR Iterative Solution for Two-sided Obstacle Problems

为了求解双边障碍问题,将SOR迭代进行投影建立投影SOR迭代算法.由此算法产生的迭代序列至少存在一个聚点,该聚点是双边障碍问题的解.并且,当矩阵为非退化对称矩阵时,该序列收敛到双边障碍问题的解.投影迭代对于双边障碍问题的理论研究和应用具有重要意义.

To solve the two-sided obstacle problem, SOR algorithm is projected to be established projective SOR algorithm. It is shown that the sequence generated by the projective SOR algorithm has an accumulation point which solves the two-sided obstacle problem. Moreover, when the matrix involved in the two-sided obstacle problem is a symmetric and nondegenerate matrix, the sequence converges to a solution of the problem. Projective iterations play a leading role in the studies of the two-sided obstacle problem and its application.