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

Speaker:Zhen-Chen Guo (Nanjing Univ)
Time: Mon. 15:20-16:20, 2020-11-9
Venue:Lecture Hall, Jin Chun Yuan West Bldg.

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.
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