報告人：曾文龍 博士

報告題目：Construction and Decomposition of Scaling Matrices for Sk-SDD Matrices and Their Application to Linear Complementarity Problems

報告時間：2025年12月6日（周六）下午5：00

報告地點：云龍校區6號樓304會議室

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

2023年6月博士畢業于湘潭大學數學專業，2023年7月至2025年7月在上海大學從事博士后研究工作，出站后進入南昌大學工作。主持國家資助博士后研究人員計劃C檔、博士后科研業績評估考核三檔資助、湖南省研究生科研創新項目(重點項目)。已在Numer. Algorithms、J. Comput. Appl. Math.、East Asian J. Appl. Math.、Appl. Math. Lett.、Linear Multilinear Algebra等SCI期刊發表論文10余篇，其中第一作者9篇。獲湖南省芙蓉學子·學術科研獎、“華為杯”中國研究生數學建模競賽二等獎等榮譽。

報告摘要：

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.