A stochastic performance model for pipelined Krylov methods

A Stochastic Performance Model for Pipelined Krylov Methods

Pipelined Krylov methods seek to ameliorate the latency due to inner products necessary for projection by overlapping it with the computation associated with sparse matrix-vector multiplication. We clarify a folk theorem that this can only result in a speedup of 2× over the naive implementation. Examining many repeated runs, we show that stochastic noise also contributes to the latency, and we ...

On the Numerical Stability Analysis of Pipelined Krylov Subspace Methods

Algebraic solvers based on preconditioned Krylov subspace methods are among the most powerful tools for large scale numerical computations in applied mathematics, sciences, technology, as well as in emerging applications in social sciences. The study of mathematical properties of Krylov subspace methods, in both the cases of exact and inexact computations, is a very active area of research and ...

Parallel Krylov Methods for Econometric Model Simulation

This paper investigates parallel solution methods to simulate large-scale macroeconometric models with forward-looking variables. The method chosen is the Newton-Krylov algorithm. We concentrate on a parallel solution to the sparse linear system arising in the Newton algorithm, and we empirically analyze the scalability of the GMRES method, which belongs to the class of so-called Krylov subspac...

A Stochastic Optimization Model for Groundwater Management

A Stochastic Model for Water Resources Management

Irrigation water management is crucial for agricultural production and livelihood security in many regions and countries throughout the world. Over the past decades, controversial and conflictladen water-allocation issues among competing municipal, industrial and agricultural interests have raised increasing concerns. Particularly, growing population, varying natural conditions and shrinking wa...