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Accurate Numerical Solution For Shifted M-Matrix Algebraic Riccati Equation

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

*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：