Several statistics-based detectors, based on unimodal matrix models, for determining the number of sources in a field are designed. A new variance ratio statistic is proposed, and its asymptotic distribution analyzed. The detector shown to outperform alternatives. It that further improvements achievable via optimally selected rotations. Numerical experiments demonstrate performance gains our de...

In this paper we consider fast numerical algorithms for solving certain modified matrix eigenvalue problems associated with algebraic equations. The matrices under consideration have the form A = T + uv , where u, v ∈ Rn×n and T = (ti,j) ∈ Rn×n is a tridiagonal matrix such that tj+1,j = ±tj,j+1, 1 ≤ j ≤ n−1. We show that the DQR approach proposed in [Uhlig F., Numer. Math. 76 (1997), no. 4, 515...

CANDECOMP/PARAFAC (CPD) approximates multiway data by sum of rank-1 tensors. Our recent study has presented a method to rank-1 tensor deflation, i.e. sequential extraction of the rank-1 components. In this paper, we extend the method to block deflation problem. When at least two factor matrices have full column rank, one can extract two rank-1 tensors simultaneously, and rank of the data tensor...

With Q q,n the distribution of n minus the rank of a matrix chosen uniformly from the collection of all n × (n + m) matrices over the finite field F q of size q ≥ 2, and Q q the distributional limit of Q q,n as n → ∞, we apply Stein's method to prove the total variation bound 1 8q n+m+1 ≤ ≤Q q,n − Q q TV ≤ 3 q n+m+1. In addition, we obtain similar sharp results for the rank distributions of sym...

A fast approximate inversion algorithm is proposed for two-level Toeplitz matrices (block Toeplitz matrices with Toeplitz blocks). It applies to matrices that can be sufficiently accurately approximated by matrices of low Kronecker rank and involves a new class of tensor-displacement-rank structured (TDS) matrices. The complexity depends on the prescribed accuracy and typically is o(n) for matr...