arXiv subjects

Eric King-wah Chu

Publications and source records attributed to Eric King-wah Chu.

2 recordsLinked to original sources

arXiv2020

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 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 triplet representations for the small M-matrix kernels in a highly accurate doubling algorithm. Illustrative numerical examples will be presented on the efficiency of our algorithm.

math.NA↗

arXiv2016

Backward Errors and Small Sample Condition Estimation for $\star$-Sylveter Equations

In this paper, we adopt a componentwise perturbation analysis for $\star$-Sylvester equations. Based on the small condition estimation (SCE), we devise the algorithms to estimate normwise, mixed and componentwise condition numbers for $\star$-Sylvester equations. We also define a componentwise backward error with a sharp and easily computable bound. Numerical examples illustrate that our algorithm under componentwise perturbations produces reliable estimates, and the new derived computable bound for the componentwise backward error is sharp and reliable for well conditioned and moderate ill-conditioned $\star$-Sylvester equations under large or small perturbations.

math.NA↗