一类新的预条件USSOR迭代法的比较定理

摘要

A novel preconditioned matrix and a new Un-Symmetrical Successive Over Relaxation (USSOR) itera-tive method base on this preconditioned matrix are proposed in this paper .T he spectral radius of the new and the traditional USSOR iterative method were compared when coefficient matrix was irreducible .The result demon-strates that the new method accelerates the speed of convergency .And a new comparison theorem is got ,distin-guished with other methods ,the comparison inequality of spectral radius is a strict inequality .Finally two nu-merical examples are given to demonstrate the correctness of the new method .%提出一种新的预条件矩阵，并给出基于该预条件的USSOR迭代法。比较了系数矩阵为不可约 L阵时，在新的预条件下USSOR迭代法和传统USSOR迭代法谱半径的大小。预条件加快了传统的USSOR迭代法的收敛速度，并得到新的比较定理。且新方法的谱半径严格小于传统方法的谱半径。最后通过数值例子验证了所得结论的正确性。