报告主题：Ostrowski-Reich定理Ostrowski-ReichTheorems
报 告 人：袁锦昀 教授（东莞理工学院、巴西科学院院士）
报告时间：2021年6月11日（周五） 16:10
会议地点：校本部G507
邀请人：王卿文
报告摘要：For every nonsingular matrix A, we show there exists a convergent splitting A = M − N with M = DQ or M = QD where Q and D are unitary and diagonal respectively. Also, if A has an LU decomposition, there exists a convergent splitting A = M − N with triangular M. An example of construction of the desired triangular matrix M is given for p-cyclic matrices. This result allows us to establish some iterative refinement methods for linear systems, which are often better than the usual iterative refinement methods with regard to complexity and storage requirements. The convergence of the refinement process is studied.