5 citations · 23 across the 12 of their papers we have counts for
12 papers
Flexible fixed-point iteration and its applications for nonsymmetric algebraic Riccati equations
Zhen-Chen Guo, Xin Liang
In this paper, we reveal the intrinsic Toeplitz structure in the unique stabilizing solution for nonsymmetric algebraic Riccati equations by employing a shift-involved fixed-point…
An RADI-type method for stochastic continuous-time algebraic Riccati equations
Zhen-Chen Guo, Xin Liang
In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-typ…
Stochastic algebraic Riccati equations are almost as easy as deterministic ones theoretically
Zhen-Chen Guo, Xin Liang
Stochastic algebraic Riccati equations, also known as rational algebraic Riccati equations, arising in linear-quadratic optimal control for stochastic linear time-invariant systems…
The intrinsic Toeplitz structure and its applications in algebraic Riccati equations
Zhen-Chen Guo, Xin Liang
In this paper we derive a Toeplitz-structured closed form of the unique positive semi-definite stabilizing solution for the discrete-time algebraic Riccati equations, especially fo…
On the Optimality of the Oja's Algorithm for Online PCA
Xin Liang
In this paper we analyze the behavior of the Oja's algorithm for online/streaming principal component subspace estimation. It is proved that with high probability it performs an ef…
Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic Riccati equations
Zhen-Chen Guo, Eric King-wah Chu, Xin Liang
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 it…
Bifurcation Analysis of the Eigenstructure of the Discrete Single-curl Operator in Three-dimensional Maxwell's Equations with Pasteur Media
Xin Liang, Zhen-Chen Guo, Tsung-Ming Huang +2
This paper focuses on studying the bifurcation analysis of the eigenstructure of the -parameterized generalized eigenvalue problem (-GEP) arising in three-dimensional (3D) so…
Decoupled Structure-Preserving Doubling Algorithm with Truncation for Large-Scale Algebraic Riccati Equations
Zhen-Chen Guo, Eric King-Wah Chu, Xin Liang +1
In \emph{Guo et al, arXiv:2005.08288}, we propose a decoupled form of the structure-preserving doubling algorithm (dSDA). The method decouples the original two to four coupled recu…
A decoupled form of the structure-preserving doubling algorithm with low-rank structures
Zhen-Chen Guo, Eric King-Wah Chu, Xin Liang +1
The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing…
Convergence Analysis of Extended LOBPCG for Computing Extreme Eigenvalues
Peter Benner, Xin Liang
This paper is concerned with the convergence analysis of an extended variation of the locally optimal preconditioned conjugate gradient method (LOBPCG) for the extreme eigenvalue o…
Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation
Xin Liang, Zhen-Chen Guo, Li Wang +2
Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of…
Relative Perturbation Theory for Quadratic Hermitian Eigenvalue Problem
Peter Benner, Xin Liang, Suzana Miodragović +1
In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form , where $…