报告人：曾文龙 博士
报告题目：Construction and Decomposition of Scaling Matrices for Sk-SDD Matrices and Their Application to Linear Complementarity Problems
报告时间：2025年12月6日（周六）下午5：00
报告地点：云龙校区6号楼304会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
2023年6月博士毕业于湘潭大学数学专业，2023年7月至2025年7月在上海大学从事博士后研究工作，出站后进入南昌大学工作。主持国家资助博士后研究人员计划C档、博士后科研业绩评估考核三档资助、湖南省研究生科研创新项目(重点项目)。已在Numer. Algorithms、J. Comput. Appl. Math.、East Asian J. Appl. Math.、Appl. Math. Lett.、Linear Multilinear Algebra等SCI期刊发表论文10余篇，其中第一作者9篇。获湖南省芙蓉学子·学术科研奖、“华为杯”中国研究生数学建模竞赛二等奖等荣誉。
报告摘要：
We introduce a novel subclass of H-matrices termed Sk-strictly diagonally dominant (Sk-SDD) matrices, where k is any positive integer. These matrices generalize SDD matrices, S-SDD matrices, and generalized SDD1 matrices. We present a method for constructing scaling matrices for Sk-SDD matrices, such that their product with the scaling matrix yields an SDD matrix. By decomposing the scaling matrix into a product of two matrices, we establish an upper bound on the infinity norm of the inverse matrix for Sk-SDD matrices. Moreover, based on this decomposition, we derive an error bound for the linear complementarity problem associated with Sk-SDD matrices. Notably, our error bound achieves a theoretical improvement over existing results. Furthermore, we demonstrate the effectiveness and superiority of our findings via numerical experiments with randomly generated matrices.