Low precision arithmetic, in particular half (16-bit) floating point is now available commercial hardware. Using lower can offer significant savings computation and communication costs with proportional energy. Motivated by this, there has been a renewed interest mixed iterative refinement schemes for solving linear systems A x = b , new variants of GMRES-based have developed. Each variant give...

To help make refinement more usable in practice we introduce a general, flexible model of refinement. This is defined in terms of what contexts an entity can appear in, and what observations can be made of it in those contexts. Our general model is expressed in terms of an operational semantics, and by exploiting the well-known isomorphism between state-based relational semantics and event-base...

The research presented in this paper is motivated by the following question. How can the generality order of clauses and the relevant concepts such as refinement be adapted to be used in a stochastic search? To address this question we introduce the concept of stochastic refinement operators and adapt a framework, called stochastic refinement search. In this paper we introduce stochastic refine...