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(diǎn)：云龍校區(qū)6號樓304會議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報告人簡介：

2023年6月博士畢業(yè)于湘潭大學(xué)數(shù)學(xué)專業(yè)，2023年7月至2025年7月在上海大學(xué)從事博士后研究工作，出站后進(jìn)入南昌大學(xué)工作。主持國家資助博士后研究人員計(jì)劃C檔、博士后科研業(yè)績評估考核三檔資助、湖南省研究生科研創(chuàng)新項(xiàng)目(重點(diǎn)項(xiàng)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(fā)表論文10余篇，其中第一作者9篇。獲湖南省芙蓉學(xué)子·學(xué)術(shù)科研獎、“華為杯”中國研究生數(shù)學(xué)建模競賽二等獎等榮譽(yù)。

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.