Excellence in Research and Innovation for Humanity

Hou Biao Li

Publications

7

Publications

7
1954
Stability of Interval Fractional-order Systems with Order 0 < α < 1
Abstract:

In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.

Keywords:
Interval fractional-order systems, linear matrix inequality (LMI), asymptotical stability.
6
3728
A Note on the Convergence of the Generalized AOR Iterative Method for Linear Systems
Abstract:

Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant cofficient matrices. J. Comp. Appl. Math. 213, 240-247 (2008)]. In this paper, we give the convergence of the GAOR method for linear systems with strictly doubly diagonally dominant matrix, which improves these corresponding results.

Keywords:
Diagonally dominant matrix, GAOR method, Linear system, Convergence
5
16754
The Convergence Results between Backward USSOR and Jacobi Iterative Matrices
Abstract:

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

Keywords:
Backward USSOR iterative matrix, Jacobi iterative matrix, convergence, spectral radius
4
16834
The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices
Abstract:

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

Keywords:
Backward MPSD iterative matrix, Jacobi iterative matrix, eigenvalue, p-cyclic matrix.
3
17064
Some Preconditioners for Block Pentadiagonal Linear Systems Based on New Approximate Factorization Methods
Abstract:

In this paper, getting an high-efficiency parallel algorithm to solve sparse block pentadiagonal linear systems suitable for vectors and parallel processors, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are appropriate when the desired target is to maximize parallelism. Moreover, some theoretical results about these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block pentadiagonal H-matrices is also described. In addition, the availability of these preconditioners is illustrated with some numerical experiments arising from two dimensional biharmonic equation.

Keywords:
Parallel algorithm, Pentadiagonal matrix, Polynomial approximate inverse, Preconditioners, Stair matrix.
2
9997825
A New Proof on the Growth Factor in Gaussian Elimination for Generalized Higham Matrices
Abstract:

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3√2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some new findings.

Keywords:
CSPD matrix, positive definite, Schur complement, Higham matrix, Gaussian elimination, Growth factor.
1
9998059
Stability Analysis of Fractional Order Systems with Time Delay
Abstract:

In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.

Keywords:
Fractional order systems, Time delay, Characteristic equation.