Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector algorithms to track many solution paths of a polynomial homotopy. The data parallelism that provides the speedups stems from the evaluation and differentiation […]

May 10, 2015 by hgpu

In non-linear systems, where explicit analytic solutions usually can’t be found, visualisation is a powerful approach which can give insights into the dynamical behaviour of models; it is also crucial for teaching this area of mathematics. In this paper we present new software, Fireflies, which exploits the power of graphical processing unit (GPU) computing to […]

May 7, 2015 by hgpu

In this paper, we propose a new very simple numerical method for solving liquid-gas compressible flows on two dimensional cartesian meshes. For achieving high performance, the scheme is tested on recent multi-core processors and Graphics Processing Units (GPU), using the OpenCL environment. We describe how to install and to run the code CLBUBBLE for computing […]

April 25, 2015 by hgpu

In a recent paper, Parikh and Boyd describe a method for solving a convex optimization problem, where each iteration involves evaluating a proximal operator and projection onto a subspace. In this paper we address the critical practical issues of how to select the proximal parameter in each iteration, and how to scale the original problem […]

April 1, 2015 by hgpu

This document describes an implementation in C of a set of randomized algorithms for computing partial Singular Value Decompositions (SVDs). The techniques largely follow the prescriptions in the article "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions," N. Halko, P.G. Martinsson, J. Tropp, SIAM Review, 53(2), 2011, pp. 217-288, but with some […]

February 22, 2015 by hgpu

In this thesis we present the first, to our knowledge, implementation and performance analysis of Hermite methods on GPU accelerated systems. We give analytic background for Hermite methods; give implementations of the Hermite methods on traditional CPU systems as well as on GPUs; give the reader background on basic CUDA programming for GPUs; discuss performance […]

February 2, 2015 by hgpu

We discuss modeling and GPU-based computation in a new class of multivariate dynamic models customized to learning and prediction with increasingly high-dimensional time series. This defines an approach to decoupling analysis into a parallel set of univariate time series dynamic models, while flexibly modeling cross-series relationships in a novel, induced class of time-varying graphical models […]

September 30, 2014 by hgpu

Kurepa’s conjecture states that there is no odd prime p which divides !p=0!+1!+…+(p-1)!. We search for a counterexample of this conjecture for all p<10^10. We introduce new optimization techniques and perform the computation using graphics processing units (GPUs). Additionally, we consider the generalized Kurepa’s left factorial given as !kn=(0!)k+(1!)k+…+((n-1)!)k and show that for all integers […]

September 3, 2014 by hgpu

We present a block structured orthogonal factorization (BSOF) algorithm and its parallelization for computing the inversion of block p-cyclic matrices.We aim at the high performance on multicores with GPU accelerators. We provide a quantitative performance model for optimal host-device load balance, and validate the model through numerical tests. Benchmarking results show that the parallel BSOF […]

August 23, 2014 by hgpu

A parallel implementation of a method of the semi-Lagrangian type for the advection equation on a hybrid architecture com-putation system is discussed. The difference scheme with variable stencil is constructed on the base of an integral equality between the neighboring time levels. The proposed approach allows one to avoid the Courant-Friedrichs-Lewy restriction on the relation […]

August 21, 2014 by hgpu

This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and […]

August 13, 2014 by hgpu

CUMODP is a CUDA library for exact computations with dense polynomials over finite fields. A variety of operations like multiplication, division, computation of subresultants, multi-point evaluation, interpolation and many others are provided. These routines are primarily designed to offer GPU support to polynomial system solvers and a bivariate system solver is part of the library. […]

August 7, 2014 by hgpu