Yiqin Lin

Order reduction of bilinear MIMO dynamical systems using new block Krylov subspaces

In this paper we study numerical methods for the model-order reduction of large-scale bilinear multi-input multi-output systems. A new projection method is proposed. The projection subspace is the union of some new block Krylov subspaces. We show that the reduced-order bilinear system constructed by the new method can match a desired number of moments of multivariable transfer functions corresponding to the kernels of Volterra series representation of the original system. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

A MODEL-ORDER REDUCTION METHOD BASED ON KRYLOV SUBSPACES FOR MIMO BILINEAR DYNAMICAL SYSTEMS

In this paper, we present a Krylov subspace based projection method for reduced-order modeling of large scale bilinear multi-input multioutput (MIMO) systems. The reduced-order bilinear system is constructed in such a way that it can match a desired number of moments of multivariable transfer functions corresponding to the kernels of Volterra series representation of the original system. Numerical examples report the effectiveness of this method.

Model-order reduction of large-scale second-order MIMO dynamical systems via a block second-order Arnoldi method

In this paper, we present a structure-preserving model-order reduction method for solving large-scale second-order MIMO dynamical systems. It is a projection method based on a block second-order Krylov subspace. We use the block second-order Arnoldi (BSOAR) method to generate an orthonormal basis of the projection subspace. The reduced system preserves the second-order structure of the original system. Some theoretical results are given. Numerical experiments report the effectiveness of this method.

Convergence analysis of a variant of the Newton method for solving nonlinear equations

The paper presents a convergence analysis of a modified Newton method for solving nonlinear systems of equations. The convergence results show that this method converges cubically in the nonsingular case, and linearly with the rate 3/8 under some sufficient conditions when the Jacobian is singular at the root. The convergence theory is used to analyze the convergence behavior when the modified Newton method is applied to a nonsymmetric algebraic Riccati equation arising in transport theory. Numerical experiment confirms the theoretical results.

Restarted generalized Krylov subspace methods for solving large-scale polynomial eigenvalue problems

In this paper, we introduce a generalized Krylov subspace

On the convergence of iterative methods for stabilized saddle point problems

{\mathcal{G}_{m}(\mathbf{A};\mathbf{u})}

On an inexact Uzawa-type algorithm for stabilized saddle point problems

based on a square matrix sequence {Aj} and a vector sequence {uj}. Next we present a generalized Arnoldi procedure for generating an orthonormal basis of

Analysis of the nonlinear Uzawa algorithm for symmetric saddle point problems

{\mathcal{G}_{m}(\mathbf{A};\mathbf{u})}

A new projection method for solving large Sylvester equations

. By applying the projection and the refined technique, we derive a restarted generalized Arnoldi method and a restarted refined generalized Arnoldi method for solving a large-scale polynomial eigenvalue problem (PEP). These two methods are applied to solve the PEP directly. Hence they preserve essential structures and properties of the PEP. Furthermore, restarting reduces the storage requirements. Some theoretical results are presented. Numerical tests report the effectiveness of these methods.

A modified Newton method for solving non-symmetric algebraic Riccati equations arising in transport theory

The convergence of the inexact Uzawa method for stabilized saddle point problems was analysed in a recent paper by Cao, Evans and Qin. We show that this method converges under conditions weaker than those stated in their paper.