In this paper, a completely real-valued approach for direction finding is developed. The proposed algorithm using high order powers of the sample covariance matrix to approximate the noise subspace in the real domain, so that the computational burden is substantially reduced and the number of incident sources is not required. Numerical simulation results demonstrate the satisfying performance o...

We consider the gradient method xt+1 = xt + γt(st + wt), where st is a descent direction of a function f : �n → � and wt is a deterministic or stochastic error. We assume that ∇f is Lipschitz continuous, that the stepsize γt diminishes to 0, and that st and wt satisfy standard conditions. We show that either f(xt) → −∞ or f(xt) converges to a finite value and ∇f(xt) → 0 (with probability 1 in t...

We consider new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with cross derivative terms. Our approach is based on the unconditionally stable ADI scheme proposed by Hundsdorfer [12]. Different numerical discretizations which lead to schemes which are fourth-order accurate in space and sec...

Acoustic sensing is a viable approach for solving issues related to many applications, namely, biomedical, distance measurements, mechanical, health infrastructure monitoring, etc. It is generally sustainable and of no negative impact on the object under test. The use of acoustic sensing under beamforming technique is an important asset to be exploited, especially for the aforementioned applica...

By a variant of the techniques introduced by the first two authors in [DF] to prove that second derivatives of solutions to the Monge-Ampère equation are locally in L logL, we obtain interior W 2,1+ε estimates.