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- Xiao-Xia Guo, Wen-Wei Lin, Shu-Fang Xu
- Numerische Mathematik
- 2006

In this paper we propose a structure-preserving doubling algorithm (SDA) for computing the minimal nonnegative solutions to the nonsymmetric algebraic Riccati equation (NARE) based on the techniques developed in the symmetric cases. This method allows the simultaneous approximation of the minimal nonnegative solutions of the NARE and its dual equation, only… (More)

- Jonq Juang, Wen-Wei Lin
- SIAM J. Matrix Analysis Applications
- 1998

We consider a nonsymmetric algebraic matrix Riccati equation arising from transport theory. The nonnegative solutions of the equation can be explicitly constructed via the inversion formula of a Cauchy matrix. An error analysis and numerical results are given. We also show a comparison theorem of the nonnegative solutions.

- Eric King-Wah Chu, Hung-Yuan Fan, Wen-Wei Lin
- SIAM J. Matrix Analysis Applications
- 2007

From the necessary and sufficient conditions for complete reachability and observability of periodic time-varying descriptor systems, the symmetric positive semi-definite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method… (More)

- Wen-Wei Lin, Volker Mehrmanny, Hongguo Xuz
- 1999

We study canonical forms for Hamiltonian and symplectic matrices or pencils under equivalence transformations which keep the class invariant. In contrast to other canonical forms our forms are as close as possible to a triangular structure in the same class. We give necessary and sufficient conditions for the existence of Hamiltonian and symplectic… (More)

- Hung-Yuan Fan, Wen-Wei Lin, Paul Van Dooren
- SIAM J. Matrix Analysis Applications
- 2004

In this paper, we propose structured doubling algorithms for the computation of the weakly stabilizing Hermitian solutions of the continuousand discrete-time algebraic Riccati equations, respectively. Assume that the partial multiplicities of purely imaginary and unimodular eigenvalues (if any) of the associated Hamiltonian and symplectic pencil,… (More)

- Wen-Wei Lin, Shu-Fang Xu
- SIAM J. Matrix Analysis Applications
- 2006

In this paper, we introduce the doubling transformation, a structure-preserving transformation for symplectic pencils, and present its basic properties. Based on these properties, a unified convergence theory for the structure-preserving doubling algorithms for a class of Riccati-type matrix equations is established, using only elementary matrix theory.

- Yu-Ling Lai, Kun-Yi Andrew Lin, Wen-Wei Lin
- Numerical Lin. Alg. with Applic.
- 1997

In this paper, we propose an inexact inverse iteration method for the computation of the eigenvalue with the smallest modulus and its associated eigenvector for a large sparse matrix. The linear systems of the traditional inverse iteration are solved with accuracy that depends on the eigenvalue with the second smallest modulus and iteration numbers. We… (More)

- Chun-Yueh Chiang, Eric King-Wah Chu, Chun-Hua Guo, Tsung-Ming Huang, Wen-Wei Lin, Shu-Fang Xu
- SIAM J. Matrix Analysis Applications
- 2009

In this paper, we review two types of doubling algorithm and some techniques for analyzing them. We then use the techniques to study the doubling algorithm for three different nonlinear matrix equations in the critical case. We show that the convergence of the doubling algorithm is at least linear with rate 1/2. As compared to earlier work on this topic,… (More)

- Wen-Wei Lin
- 2001

This paper is devoted to perturbation analysis for the eigenproblem of periodic matrix pairs {(Aj ,Ej )}j=1. We first study perturbation expansions of periodic deflating subspaces and eigenvalue pairs. Then, we derive explicit expressions of condition numbers, perturbation bounds and backward errors for eigenvalue pairs and periodic deflating subspaces. ©… (More)