To describe the dynamics of stage-structured populations with m stages living in n patches, we consider matrix models of the form SD, where S is a block diagonal matrix with n× n column substochastic matrices S1, . . . , Sm along the diagonal and D is a block matrix whose blocks aren× n nonnegative diagonal matrices. The matrix S describes movement between patches and the matrix D describes gro...

We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes n × n zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e. features a right-hand side with a nested commutator of matrices, and structurally resembles the double-bracket o.d.e. studied by R.W. Brockett in 1991. We prove that its solutions converge asymptotical...

In computational electromagnetics, we consider preconditioning techniques combined with the Krylov iterative methods to solve large dense linear systems, where the coefficient matrix are complex-valued matrix arising from discretizd hybrid integral equations. Due to its easy implementation, the block diagonal preconditioner has been used to accelerate the convergence rate of Krylov iterative me...

Let an n x -matrix A have m < (m ? 2) different eigenvalues ?j of the algebraic multiplicity (j = 1,..., m). It is proved that there are ?j-matrices Aj, each which has a unique eigenvalue ?j, such similar to block-diagonal matrix ?D diag (A1,A2,..., Am). I.e. invertible T, T-1AT ?D. Besides, sharp bound for number kT := ||T||||T-1|| derived. As applications these results we obtain norm estim...

Every n×n generalized K-centrosymmetric matrix A can be reduced into a 2× 2 block diagonal matrix (see [20]). This block diagonal matrix is called the reduced form of the matrix A. In this paper we further investigate some properties of the reduced form of these matrices and discuss the square roots of these matrices. Finally exploiting these properties, the development of structure-preserving ...

Research is ongoing that examines parallel direct block-diagonal-bordered sparse linear solvers for irregular sparse matrix problems derived from electrical power system applications. Parallel block-diagonal-bordered sparse linear solvers exhibit distinct advantages when compared to current general parallel direct sparse matrix solvers. Our research shows that actual power system matrices can b...

We consider applying the preconditioned conjugate gradient (PCG) method to solve linear systems Ax = b where the matrix A comes from the discretization of second-order elliptic operators. Let (L +)) ?1 (L t +) denote the block Cholesky factorization of A with lower block triangular matrix L and diagonal block matrix. We propose a preconditioner M = (^ L +)) ?1 (^ L t +) with block diagonal matr...

Probabilistic mixture models are among the most important clustering methods. These models assume that the feature vectors of the samples can be described by a mixture of several components. Each of these components follows a distribution of a certain form. In recent years, there has been an increasing amount of interest and work in similarity-matrix-based methods. Rather than considering the f...

An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition SVD of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible ...