The paper presented a novel method to speed up the likelihood computation of the speech recognition system based continuous Hidden Markov Model (CHMM). The block-diagonal covariance matrices were applied in the method and the technique to construct an optimal block-diagonal matrix was introduced. The experimental results demonstrated that the block-diagonal covariance matrices could achieve a l...

We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix Möbius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. The...

We examine stochastic dynamical systems where the transition matrix, Φ, and the system noise, ΓQΓ T , covariance are nearly block diagonal. When H TR−1H is also nearly block diagonal, where R is the observation noise covariance and H is the observation matrix, our suboptimal filter/smoothers are always positive semidefinite, and have improved numerical properties. Applications for distributed d...

Factorizations of Wiener–Hopf type are considered in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups, with a non-archimedean linear order on the dual group. A criterion for factorizability is established for 2 × 2 block triangular matrix functions with elementary functions on the main diagonal and a binomial expression in the off-diagonal...

We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization PAP = LDL where P is a permutation matrix, L is lower triangular with a unit diagonal and D is symmetric block diagonal with 1×1 and 2×2 antidiagonal blocks. The novel algorithm requires O(n2rω−2) arithmetic o...

The main goal of this article is to establish several new \({\mathbb {A}}\)-numerical radius equalities for \(n\times n\) circulant, skew imaginary tridiagonal, and anti-tridiagonal operator matrices, where {A}}\) the diagonal matrix whose entries are positive bounded A. Some special cases our results lead earlier works in literature, which shows that more general. Further, some pinching type i...

Abstract. In this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers and this fixe...