Error analysis of recurrence equations

Converting Affine Recurrence Equations to Quasi-Uniform Recurrence Equations

Most work on the problem of synthesizing a systolic array from a system of recurrence equations is restricted to systems of uniform recurrence equations. Recently, researchers have begun to relax this restriction to include systems of affine recurrence equations. A system of uniform recurrence equations typically can be embedded in spacetime so that the distance between a variable and a depende...

Hierarchical Static Analysis Of Structured Systems Of Affine Recurrence Equations

The Alpha language, based on systems of affine recurrence equations over polyhedral domains, allows the expression of complex algorithms as hierarchical, parameterized structures of such systems. This paper discusses the static analysis of Alpha programs, an extended type-checking process based on the single assignment rule. We present techniques ensuring, on one hand, that a system is valid (w...

Fuzzy Galerkin method for solving Fredholm integral equations with error analysis

Random Recurrence Equations

We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(1) and GARCH(1,1) time series models. Our results build upon work of Goldie [Ann. Appl. Probab. 1 (1991) 126–166], who ha...

Structured Scheduling of Recurrence Equations

We study scheduling of structured systems of recurrence equations. We rst recall the formalism of structured systems of recurrence equations, then we explain how to implement a scheduling tool for non-structured systems of reccurence equations. We introduce the notion of structured schedule and propose criteria for determining whether a structured system of reccurence equations admits a structu...