Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic

组织者 Organizer:Zhen-Chen Guo (Nanjing Univ)
时间 Time: 周一15:20-16:20, 2020-11-9
地点 Venue:近春园西楼第三会议室

讨论班简介 Description

Title: Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic Riccati equations
We consider the numerical solution of large-scale M-matrix algebraic Riccati equations (MAREs) with low-rank structures. We derive a new doubling iteration, decoupling the four original iteration formulae in the alternating-directional doubling algorithm. We prove that the kernels in the decoupled algorithm are small M-matrices. Illumined by the highly accurate algorithm proposed by Xue and Li in 2017, we construct the novel triplet representations for the small M-matrix kernels in a highly accurate doubling algorithm. With these triplet representations, we develop a highly accurate doubling algorithm, named dADDA, for large-scale MAREs with low-rank structures, where the GTH-like algorithm is applied for solving the associated linear systems. Illustrative numerical examples will be presented on the efficiency of our algorithm.