*主持人：潘建瑜 教授
*讲座内容简介：
An algebraic Riccati (ARE) equation is called a shifted $M$-matrix algebraic Riccati equation (MARE) if it can be turned into an MARE after its matrix variable is partially shifted by a diagonal matrix. Such an ARE can arise from computing the invariant density of a Markov modulated Brownian motion. Sufficient and necessary conditions for an ARE to be a shifted MARE are obtained. Based on the condition,a highly accurate implementation of the alternating directional doubling algorithm (ADDA) is established to compute the extremal solution of a shifted MARE, as well as a quantity needed for computing the invariant density in the application, with high entrywise relative accuracy. Numerical examples are presented to demonstrate the theory and algorithms.
*主讲人简介：
薛军工，复旦大学168幸运飞艇计划
教授，博士生导师，计算数学方向，目前担任复旦大学168幸运飞艇计划
副院长；1990年、1996年先后在复旦大学获得学士、理学博士学位；2004年4月至今任职复旦大学教授；1999年德国洪堡基金、2004年入选教育部新世纪优秀人才支持计划，2018 年获评复旦大学研究生心目中的好导师。
