Accurate Numerical Solution for Shifted M-Matrix Algebraic Riccati Equations

Changli Liu, Jungong Xue, Ren-Cang Li*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


An algebraic Riccati equation (ARE) 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 conditions, 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.
Original languageEnglish
JournalJournal of Scientific Computing
Issue number15
Publication statusPublished - Jul 2020


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