In this paper we propose a novel adaptation algorithm for Filterand-Sum beamforming in spatially correlated noise. Deterministic and stochastic gradient ascent algorithms are derived from a constrained optimization problem, which iteratively estimate the principal eigenvector of a generalized eigenvalue problem. The method does not require an explicit estimation of the speaker location. It is s...

We prove certain gradient and eigenvalue estimates, as well the heat kernel for Hodge Laplacian on (m, 0) forms, i.e., sections of canonical bundle Kähler manifolds, where m is complex dimension manifold. Instead usual dependence curvature tensor, our condition depends only Ricci bound. The proof based a new Bochner type formula which involves scalar curvature.

A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop...

We consider complex clustered networks with a gradient structure, where the sizes of the clusters are distributed unevenly. Such networks describe actual networks in biophysical systems and in technological applications more closely than the previous models. Theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field, but only when the...

<p style='text-indent:20px;'>This paper proposes a nonmonotone spectral gradient method for solving large-scale unconstrained optimization problems. The parameter is derived from the eigenvalues of an optimally sized memoryless symmetric rank-one matrix obtained under measure defined as ratio determinant updating over its largest eigenvalue. Coupled with line search strategy where backtra...

We present an iterative method to compute the Maxwell’s transmission eigenvalue problem which has importance in non-destructive testing of anisotropic materials. The transmission eigenvalue problem is first written as a quad-curl eigenvalue problem. Then we show that the real transmission eigenvalues are the roots of a non-linear function whose value is the generalized eigenvalue of a related s...

Many classes of singularly perturbed reaction-diiusion equations possess localized solutions where the gradient of the solution is large only in the vicinity of certain points or interfaces in the domain. The problems of this type that are considered are an interface propagation model from materials science and an activator-inhibitor model of morphogenesis. These two models are formulated as no...

In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure evaluations is accomplished by a combination of a fast mixed variational eigenvalue solver and distributed Graphic Processing Unit (GPU) parallel computation...

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bou...