An abstract formulation of variational refinement

An abstract formulation of variational refinement

In this paper, the theory of abstract splines is applied to the variational refinement of (periodic) curves that meet data to within convex sets in IR. The analysis is relevant to each level of refinement (the limit curves are not considered here). The curves are characterized by an application of a separation theorem for multiple convex sets, and represented as the solution of an equation invo...

Refinement of an Abstract Model of MSG

This report describes the second phase of an experiment designed to demonstrate techniques for software development and evolution. The experiment involves the production of a family of functionally similar systems on dissimilar host computers with markedly different operating systems. The basic technique used is machine-assisted stepwise refinement from an abstract model program that embodies t...

Variational Formulation of Problems and Variational Methods

Nonuniform Variational Interpolatory Refinement

In this paper we investigate certain properties of the curves sk generated by a non-uniform variational refinement scheme defined over a k-window of some bi-infinite sequence of points. In particular, we show that error between sn and sk for k ≪ n over some fixed interval decays exponentially as k ↑ n, showing that sn can be well-approximated by sk for k much smaller than n. We use this result ...

Purity Analysis: An Abstract Interpretation Formulation

Salcianu and Rinard present a compositional purity analysis that computes a summary for every procedure describing its side-effects. In this paper, we formalize a generalization of this analysis as an abstract interpretation, present several optimizations and an empirical evaluation showing the value of these optimizations. The Salcianu-Rinard analysis makes use of abstract heap graphs, similar...