An iterative approach for joint optimization of a scalar error-feedback matrix and a coordinate transformation matrix is developed to minimize the roundoff noise subject to the l2-norm dynamic-range scaling constraints. When the iterative algorithm converges and the optimal coordinate transformation matrix is obtained, the diagonal error-feedback matrix is derived to minimize the noise gain in ...

Lyapunov equations with low-rank right-hand sides often have solutions whose singular values decay rapidly, enabling iterative methods that produce low-rank approximate solutions. All previously known bounds on this decay involve quantities that depend quadratically on the departure of the coefficient matrix from normality: these bounds suggest that the larger the departure from normality, the ...

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

The inertia of a Hermitian matrix is defined to be a triplet composed by the numbers of the positive, negative and zero eigenvalues of the matrix counted with multiplicities, respectively. In this paper, we give various closed-form formulas for the maximal and minimal values for the rank and inertia of the Hermitian expression A + X, where A is a given Hermitian matrix and X is a variable Hermi...

We consider two types of spiked multivariate F distributions: a scaled distribution with the scale matrix equal to a rank-k perturbation of the identity, and a distribution with trivial scale, but rank-k non-centrality. The eigenvalues of the rank-r matrix (spikes) parameterize the joint distribution of the eigenvalues of the corresponding F matrix. We show that, for the spikes located above a ...

A generalized directions-of-arrival (DOAs) estimation algorithm is developed for the rank-one (point source) and higher-rank (distributed source) signal models. For higher-rank signals, the integral steering vector is deduced to be a Schur-Hadamard product comprising the steering vector of rank-one source and a real matrix according to the symmetry assumption of angular signal intensity. And th...