We present an algebraic multilevel method that is based on sparse approximate inverse matrices. The approach is based on the observation that sparse approximate inverses based on norm minimization [4,3,2] can easily be adapted such that they approximate the operator quite well on a large subspace. A natural consequence is to augment the sparse approximate inverse with a correction term of small...

In this paper, we provide a framework for calculating expected utility in models with chaotic equilibria and consequently a framework for ranking chaos. Suppose that a dynamic economic model’s equilibria correspond to orbits generated by a chaotic dynamical system f : X → X where X is a compact metric space and f is continuous. The map f could represent the forward dynamics xt+1 = f(xt) or the ...

Any learning algorithm over Markov decision processes (MDPs) will have worst-case regret Ω( √ SAT ) where T is the elapsed time and S and A are the cardinalities of the state and action spaces. In many settings of interest S and A may be so huge that it is impossible to guarantee good performance for an arbitrary MDP on any practical timeframe T . We show that, if we know the true system can be...

Propositional STRIPS planning problems can be viewed as nite state automata (FSAs) represented in a factored form. Automaton minimization is a well-known technique for reducing the size of an explicit FSA. Recent work in computer-aided veriication on model checking has extended this technique to provide automaton minimization algorithms for fac-tored FSAs. In this paper, we consider the relatio...

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better th...

We propose two coding schemes for distributed matrix multiplication in the presence of stragglers. These are adaptations Luby Transform (LT) codes and Raptor to termed Factored LT (FLT) codes (FRT) . show that all nodes Tanner graph a randomly sampled code have tree-like neighborhood with high ...

The standard Incomplete LU (ILU) preconditioners often fail for general sparse indeenite matrices because they give rise tòunstable' factors L and U. In such cases, it may be attractive to approximate the inverse of the matrix directly. This paper focuses on approximate inverse preconditioners based on minimizing kI?AMk F , where AM is the preconditioned matrix. An iterative descent-type method...