Aiming to fully exploit the computing power of all CPUs and all GPUs on hybrid CPU-GPU systems to solve dense linear algebra problems, we design a class of heterogeneous tile algorithms to maximize the degree of parallelism, to minimize the communication volume, as well as to accommodate the heterogeneity between CPUs and GPUs. The new […]

August 1, 2014 by hgpu

Lossless data compression is used to reduce storage requirements, allowing for the relief of I/O channels and better utilization of bandwidth. The Lempel-Ziv lossless compression algorithms form the basis for many of the most commonly used compression schemes. General purpose computing on graphic processing units (GPGPUs) allows us to take advantage of the massively parallel […]

July 29, 2014 by hgpu

Parallel computing is a topic that became very popular in the last few decades. Parallel computers are being used in many different areas of science such as astrophysics, climate modelling, quantum chemistry, fluid dynamics and medicine. Parallel programming is a type of programming where computations can be performed concurrently on different processors or devices. There […]

July 7, 2014 by hgpu

In this paper we present new hybrid CPU-GPU routines to accelerate the solution of linear systems, with band coefficient matrix, by off-loading the major part of the computations to the GPU and leveraging highly tuned implementations of the BLAS for the graphics processor. Our experiments with an nVidia S2070 GPU report speed-ups up to 6x […]

June 23, 2014 by hgpu

Currently, state of the art libraries, like MAGMA, focus on very large linear algebra problems, while solving many small independent problems, which is usually referred to as batched problems, is not given adequate attention. In this paper, we proposed a batched Cholesky factorization on a GPU. Three algorithms – nonblocked, blocked, and recursive blocked – […]

June 12, 2014 by hgpu

We show how the cofactorization step, a compute-intensive part of the relation collection phase of the number field sieve (NFS), can be farmed out to a graphics processing unit. Our implementation on a GTX 580 GPU, which is integrated with a state-of-the-art NFS implementation, can serve as a cryptanalytic co-processor for several Intel i7-3770K quad-core […]

June 3, 2014 by hgpu

This paper presents a new fine-grained parallel algorithm for computing an incomplete LU factorization. All nonzeros in the incomplete factors can be computed in parallel and asynchronously, using one or more sweeps that iteratively improve the accuracy of the factorization. Unlike existing parallel algorithms, the new algorithm does not depend on reordering the matrix. Numerical […]

May 17, 2014 by hgpu

A version of the H-LU factorization is introduced, based on the individual computational tasks occurring during the block-wise H-LU factorization. The dependencies between these tasks form a directed acylic graph, which is used for efficient scheduling on parallel systems. The algorithm is especially suited for many-core processors and shows a much improved parallel scaling behavior […]

March 14, 2014 by hgpu

We study the impact of non-uniform memory accesses (NUMA) on the solution of dense general linear systems using an LU factorization algorithm. In particular we illustrate how an appropriate placement of the threads and memory on a NUMA architecture can improve the performance of the panel factorization and consequently accelerate the global LU factorization. We […]

March 12, 2014 by hgpu

We present a performance analysis of a parallel implementation of both conjugate gradient and preconditioned conjugate gradient solvers using graphic processing units with CUDA parallel programming model. The solvers were optimized for a fast solution of sparse systems of equations arising from Finite Element Analysis (FEA) of electromagnetic phenomena. The preconditioners were Incomplete Cholesky factorization […]

March 12, 2014 by hgpu

We present an efficient and scalable programming model for the development of linear algebra in heterogeneous multi-coprocessor environments. The model incorporates some of the current best design and implementation practices for the heterogeneous acceleration of dense linear algebra (DLA). Examples are given as the basis for solving linear systems’ algorithms – the LU, QR, and […]

February 28, 2014 by hgpu

Iterative solvers for sparse linear systems often benefit from using preconditioners. While there are implementations for many iterative methods that leverage the computing power of accelerators, porting the latest developments in preconditioners to accelerators has been challenging. In this paper we develop a self-adaptive multi-elimination preconditioner for graphics processing units (GPUs). The preconditioner is based […]

February 23, 2014 by hgpu