Open Science Research Excellence

Yiqin Lin

Publications

4

Publications

4
2067
A Schur Method for Solving Projected Continuous-Time Sylvester Equations
Abstract:
In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.
Keywords:
Projected Sylvester equation, Schur factorization,Spectral projection, Direct method.
3
9935
Restarted Generalized Second-Order Krylov Subspace Methods for Solving Quadratic Eigenvalue Problems
Abstract:
This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and present a generalized second-order Arnoldi process for constructing an orthonormal basis of the generalized second-order Krylov subspace. Then, by using the projection technique and the refined projection technique, we propose a restarted generalized second-order Arnoldi method and a restarted refined generalized second-order Arnoldi method for computing some eigenpairs of largescale quadratic eigenvalue problems. Some theoretical results are also presented. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.
Keywords:
Quadratic eigenvalue problem, Generalized secondorder Krylov subspace, Generalized second-order Arnoldi process, Projection technique, Refined technique, Restarting.
2
15709
A Projection Method Based on Extended Krylov Subspaces for Solving Sylvester Equations
Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords:
Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.
1
10009769
Multilevel Arnoldi-Tikhonov Regularization Methods for Large-Scale Linear Ill-Posed Systems
Abstract:
This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.
Keywords:
Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.