Nonlinear iterative methods and parallel computation

Newton Two-stage Parallel Iterative Methods for Nonlinear Problems

Two-stage parallel Newton iterative methods to solve nonlinear systems of the form F (x) = 0 are introduced. These algorithms are based on the multisplitting technique and on the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix F ′(x) is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms ...

Parallel S.O.R. iterative methods

New explicit group S.O.R. methods suitable for use on an asynchronous MIMD computer are presented for the numerical solution of the sparse linear systems derived from the discretization of two-dimensional , second-order, elliptic boundary value problems. A comparison with existing implicit line S.O.R. schemes for the Dirichlet model problem shows the new schemes to be superior (Barlow and Evans...

Exploring Iterative and Parallel Human Computation Processes

Mechanical Turk (MTurk) is an increasingly popular web service for paying people small rewards to do human computation tasks. Current uses of MTurk typically post independent parallel tasks. This research explores an alternative iterative paradigm, in which workers build on each other's work. We run a couple of experiments comparing the efficacy of this paradigm in two different problem domains...

Proposal 1 Optimizing parallel iterative graph computation

I propose to develop a deterministic parallel framework for performing iterative computation on a graph which schedules work on vertices based upon a valid coloring. Preliminary work modifying Graphlab, a parallel framework for implementing iterative machine learning algorithms on data graphs, has demonstrated the merits of this approach by improving performance and eliminating non-determinism....

Iterative Methods for Linear and Nonlinear Equations