The solution of linear systems equations is a central task in number scientific and engineering applications. In many cases the may take most simulation time thus representing major bottleneck further development technical software. For large scale simulations, nowadays accounting for several millions or even billions unknowns, it quite common to resort preconditioned iterative solvers exploiti...

We consider the backward error associated with a given approximate solution of a linear least squares problem. The backward error can be very expensive to compute, as it involves the minimal singular value of certain matrix that depends on the problem data and the approximate solution. An estimate based on a regularized projection of the residual vector has been proposed in the literature and a...

This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MD...

There has been much excitement recently over the use of approximate inverses for parallel preconditioning. The preconditioning operation is simply a matrix-vector product, and in the most popular formulations, the construction of the approximate inverse seems embarassingly parallel. However, diiculties arise in practical parallel implementations. This paper will survey approximate inverse preco...

We propose a novel approach for computing weakest liberal safe preconditions of programs. The standard approaches, which call for either underapproximation of a greatest fixed point, or complementation of a least fixed point, are often difficult to apply successfully. Our approach relies on a different decomposition of the weakest precondition of loops. We exchange the greatest fixed point for ...

The key components of an intelligent vehicular collision-avoidance system are sensing, evaluation, and decision making. We focus on the latter task of finding (approximately) optimal collision-avoidance control policies, a problem naturally modeled as a Markov decision process. However, standard MDP models scale exponentially with the number of state features, rendering them inept for large-sca...

The problem of belief tracking in the presence of stochastic actions and observations is pervasive and yet computationally intractable. In this work we show however that probabilistic beliefs can be maintained in factored form exactly and efficiently across a number of causally closed beams, when the state variables that appear in more than one beam obey a form of backward determinism. Since co...

The age of the air-tight hardware abstraction is over. As the computing ecosystem moves beyond the predictable yearly advances of Moore’s Law, appeals to familiarity and backwards compatibility will become less convincing: fundamental shifts in abstraction and design will look more enticing. It is time to embrace hardware–software co-design in earnest, to cooperate between programming languages...