Given A, B, C, and D, block Toeplitz matrices, we will prove the necessary sufficient condition for AB - CD = 0, to be a matrix. In addition, with respect change of basis, characterization normal matrices entries from algebra diagonal is also obtained.

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To reduce the number of parameters to estimate in the model, we propose a non-asymptotic model selection procedure supported by strong theoretical guarantees based ...

Abstract. Consider a set of square real matrices of the same size A = {A1, A2, . . . , AN}, where each matrix is partitioned, in the same way, into blocks such that the diagonal ones are square matrices. Under the assumption that the diagonal blocks in the same position have a common Lyapunov solution, sufficient conditions for the existence of a common Lyapunov solution with block diagonal str...

Compressed sensing (CS) is a rising focus in recent years for its simultaneous sampling and compression of sparse signals. Speech signals can be considered approximately sparse or compressible in some domains for natural characteristics. Thus, it has great prospect to apply compressed sensing to speech signals. This paper is involved in three aspects. Firstly, the sparsity and sparsifying matri...

Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matri...

The Kronecker structure of a hierarchical Markovian model (HMM) induces nested block partitionings in the transition matrix of its underlying Markov chain. This paper shows how sparse real Schur factors of certain diagonal blocks of a given partitioning induced by the Kronecker structure can be constructed from smaller component matrices and their real Schur factors. Furthermore, it shows how t...

We present fast and numerically stable algorithms for the solution of linear systems of equations, where the coefficient matrix can be written in the form of a banded plus semiseparable matrix. Such matrices include banded matrices, banded bordered matrices, semiseparable matrices, and block-diagonal plus semiseparable matrices as special cases. Our algorithms are based on novel matrix factoriz...

Given an undamped gyroscopic system GðλÞ 1⁄4 Mλ þ CλþK with M , K symmetric and C skew-symmetric, this paper presents a real-valued spectral decomposition of GðλÞ by a real standard pair ðX;TÞ and a skew-symmetric parameter matrix S . When T is assumed to be a block diagonal matrix, the parameter matrix S has a special structure. This spectral decomposition is applied to solve the quadratic inv...

We propose a new method for finding a parallel ordering needed in the parallel two-sided block-Jacobi EVD/SVD method. For a given matrix A, partitioned into block columns and block rows, such an ordering defines the subproblems that are solved in parallel in each parallel iteration step. Our approach is based on modeling the matrix block partition as a complete, edge-weighted graph, where the w...

We present an efficient block preconditioner for the two-dimensional biharmonic Dirichlet problem discretized by C1 bicubic Hermite finite elements. In this formulation each node in the mesh has four different degrees of freedom (DOFs). Grouping DOFs of the same type together leads to a natural blocking of the Galerkin coefficient matrix. Based on this block structure, we develop two preconditi...