Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studie...

This work presents cost-effective low-rank techniques for designing robust adaptive beamforming (RAB) algorithms. The proposed algorithms are based on the exploitation of the cross-correlation between the array observation data and the output of the beamformer. Firstly, we construct a general linear equation considered in large dimensions whose solution yields the steering vector mismatch. Then...

Many applications require the solution of multiple linear systems that have the same coeecient matrix, but diier in their right-hand sides. Instead of applying an iterative method to each of these systems individually, it is more eecient to employ a block version of the method that generates iterates for all the systems simultaneously. In this paper, we propose a block version of Freund and Nac...

The method of conjugate gradients provides a very effective way to optimize large, deterministic systems by gradient descent. In its standard form, however, it is not amenable to stochastic approximation of the gradient. Here we explore ideas from conjugate gradient in the stochastic (online) setting, using fast Hessian-gradient products to set up low-dimensional Krylov subspaces within individ...

The convergence behavior of a number of algorithms based on minimizing residual norms over Krylov subspaces, is not well understood. Residual or error bounds currently available are either too loose or depend on unknown constants which can be very large. In this paper we take another look at traditional as well as alternative ways of obtaining upper bounds on residual norms. In particular, we d...