Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416159 | Linear Algebra and its Applications | 2016 | 12 Pages |
Abstract
We further study algebraic Riccati equations associated with regular singular M-matrices. An M-matrix M is said to be regular if Mvâ¥0 for some v>0, so every irreducible singular M-matrix is a regular singular M-matrix. We prove a property about the product of the minimal nonnegative solution of such an algebraic Riccati equation and the minimal nonnegative solution of its dual equation. In the critical case, we show that the alternating-directional doubling algorithm (which includes the structure-preserving double algorithm as a special case) has linear convergence with rate 1/2. The results enhance our understanding of the behaviour of doubling algorithms for finding the minimal nonnegative solutions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chun-Hua Guo, Di Lu,