5 citations · 15 across the 14 of their papers we have counts for
14 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…
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…
Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem
Zhen-Chen Guo, Eric King-Wah Chu, Wen-Wei Lin
The discretized Bethe-Salpeter eigenvalue problem arises in the Green's function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue…
Structure-Preserving ΓQR and Γ-Lanczos Algorithms for Bethe-Salpeter Eigenvalue Problems
Zhen-Chen Guo, Tiexiang Li, Ying-Ying Zhou
To solve the Bethe-Salpeter eigenvalue problem with distinct sizes, two efficient methods, called ΓQR algorithm and Γ-Lanczos algorithm, are proposed in this paper. Both algorithms…
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…
Schur Method for Robust Pole Assignment of Descriptor Systems via Proportional Plus Derivative State Feedback
Zhen-Chen Guo
The pole assignment problem for descriptor systems is a classical inverse algebraic eigenvalue problem, which has attracted attention for decades. In this paper, we propose a direc…
Refined Schur Method for Robust Pole Assignment with Repeated Poles
Zhen-Chen Guo, Jiang Qian, Yun-feng Cai +1
Schur-type methods in \cite{Chu2} and \cite{GCQX} solve the robust pole assignment problem by employing the departure from normality of the closed-loop system matrix as the measure…
A Modified Schur Method for Robust Pole Assignment in State Feedback Control
Guo Zhen-chen, Cai Yun-feng, Qian Jiang +1
Recently, a \textbf{SCHUR} method was proposed in \cite{Chu2} to solve the robust pole assignment problem in state feedback control. It takes the departure from normality of the cl…