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Accurate Numerical Solution For Shifted M-Matrix Algebraic Riccati Equation
薛军工 教授(复旦大学)
2021年6月16日10:30-11:30  闵行数学楼102报告厅

*主持人:潘建瑜 教授


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.


薛军工,复旦大学数学科学学院教授,博士生导师,计算数学方向,目前担任复旦大学数学科学学院副院长;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。