The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to der...The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to derive a number of properties for pseudo Laguerre matrix polynomials.展开更多
Recently we have developed an eigenvector method (EVM) which can achieve the blind deconvolution (BD) for MIMO systems. One of attractive features of the proposed algorithm is that the BD can be achieved by calculatin...Recently we have developed an eigenvector method (EVM) which can achieve the blind deconvolution (BD) for MIMO systems. One of attractive features of the proposed algorithm is that the BD can be achieved by calculating the eigenvectors of a matrix relevant to it. However, the performance accuracy of the EVM depends highly on computational results of the eigenvectors. In this paper, by modifying the EVM, we propose an algorithm which can achieve the BD without calculating the eigenvectors. Then the pseudo-inverse which is needed to carry out the BD is calculated by our proposed matrix pseudo-inversion lemma. Moreover, using a combination of the conventional EVM and the modified EVM, we will show its performances comparing with each EVM. Simulation results will be presented for showing the effectiveness of the proposed methods.展开更多
Pooling design is a mathematical tool in many application areas. In this paper, we give a new construction of pooling design with subspaces of the pseudo-symplectic space and discuss its properties. We define the desi...Pooling design is a mathematical tool in many application areas. In this paper, we give a new construction of pooling design with subspaces of the pseudo-symplectic space and discuss its properties. We define the design parameters of a d^2-disjunct matrix. Then we discuss the change law of the design parameters in our construction along with their variables.展开更多
In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this ...In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this paper is to present the formulation of a two-level decomposition scheme for decoupling the linear system obtained from the discretization into independent subsystems. This scheme takes advantage of the homogeneity property of the physical problem along one direction to reduce a 2D problem to several 1D problems via a block diagonalization approach and the reflexivity property along the second direction to decompose each of the 1D problems to two independent subproblems using a reflexive decomposition, effectively doubling the number of subproblems. Based on the special structure of the coefficient matrix of the linear system derived from the discretization and a reflexivity property of the second-order Chebyshev differentiation matrix, we show that the decomposed submatrices exhibits a similar property, enabling the system to be decomposed using reflexive decompositions. Explicit forms of the decomposed submatrices are derived. The decomposition not only yields more efficient algorithm but introduces coarse-grain parallelism. Furthermore, it preserves all eigenvalues of the original matrix.展开更多
文摘The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to derive a number of properties for pseudo Laguerre matrix polynomials.
文摘Recently we have developed an eigenvector method (EVM) which can achieve the blind deconvolution (BD) for MIMO systems. One of attractive features of the proposed algorithm is that the BD can be achieved by calculating the eigenvectors of a matrix relevant to it. However, the performance accuracy of the EVM depends highly on computational results of the eigenvectors. In this paper, by modifying the EVM, we propose an algorithm which can achieve the BD without calculating the eigenvectors. Then the pseudo-inverse which is needed to carry out the BD is calculated by our proposed matrix pseudo-inversion lemma. Moreover, using a combination of the conventional EVM and the modified EVM, we will show its performances comparing with each EVM. Simulation results will be presented for showing the effectiveness of the proposed methods.
基金This work is supported by the Chinese Outstanding Youth Foundation (No. 69925308) Program for Changjiang Scholars and Innovative Research Team in University.
基金Supported by the NSF of Hebei Province(A2009000253)
文摘Pooling design is a mathematical tool in many application areas. In this paper, we give a new construction of pooling design with subspaces of the pseudo-symplectic space and discuss its properties. We define the design parameters of a d^2-disjunct matrix. Then we discuss the change law of the design parameters in our construction along with their variables.
文摘In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this paper is to present the formulation of a two-level decomposition scheme for decoupling the linear system obtained from the discretization into independent subsystems. This scheme takes advantage of the homogeneity property of the physical problem along one direction to reduce a 2D problem to several 1D problems via a block diagonalization approach and the reflexivity property along the second direction to decompose each of the 1D problems to two independent subproblems using a reflexive decomposition, effectively doubling the number of subproblems. Based on the special structure of the coefficient matrix of the linear system derived from the discretization and a reflexivity property of the second-order Chebyshev differentiation matrix, we show that the decomposed submatrices exhibits a similar property, enabling the system to be decomposed using reflexive decompositions. Explicit forms of the decomposed submatrices are derived. The decomposition not only yields more efficient algorithm but introduces coarse-grain parallelism. Furthermore, it preserves all eigenvalues of the original matrix.
