CAJ | 학술논문

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。
제출일충신적예조건구진，병급출기우해예조건적USSOR질대법。비교료계수구진위불가약 L진시，재신적예조건하USSOR질대법화전통USSOR질대법보반경적대소。예조건가쾌료전통적USSOR질대법적수렴속도，병득도신적비교정리。차신방법적보반경엄격소우전통방법적보반경。최후통과수치례자험증료소득결론적정학성。
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 .