Related papers: Accelerating Mixed-Precision Out-of-Core Cholesky …
We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block…
Cholesky factorization is a widely used method for solving linear systems involving symmetric, positive-definite matrices, and can be an attractive choice in applications where a high degree of numerical stability is needed. One such…
Geostatistics represents one of the most challenging classes of scientific applications due to the desire to incorporate an ever increasing number of geospatial locations to accurately model and predict environmental phenomena. For example,…
Sparse linear algebra routines are fundamental building blocks of a large variety of scientific applications. Direct solvers, which are methods for solving linear systems via the factorization of matrices into products of triangular…
This paper presents a GPU-accelerated framework for solving block tridiagonal linear systems that arise naturally in numerous real-time applications across engineering and scientific computing. Through a multi-stage permutation strategy…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…
We propose an efficient distributed out-of-memory implementation of the Non-negative Matrix Factorization (NMF) algorithm for heterogeneous high-performance-computing (HPC) systems. The proposed implementation is based on prior work on…
Tile low rank representations of dense matrices partition them into blocks of roughly uniform size, where each off-diagonal tile is compressed and stored as its own low rank factorization. They offer an attractive representation for many…
Cache partitioning techniques have been successfully adopted to mitigate interference among concurrently executing real-time tasks on multi-core processors. Considering that the execution time of a cache-sensitive task strongly depends on…
Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix…
Advances in GPU compute throughput and memory capacity brings significant opportunities to a wide range of workloads. However, efficiently utilizing these resources remains challenging, particularly because diverse application…
This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle…
Scalable QR factorization algorithms for solving least squares and eigenvalue problems are critical given the increasing parallelism within modern machines. We introduce a more general parallelization of the CholeskyQR2 algorithm and show…
A modern GPU aims to simultaneously execute more warps for higher Thread-Level Parallelism (TLP) and performance. When generating many memory requests, however, warps contend for limited cache space and thrash cache, which in turn severely…
In this paper we present a novel algorithm developed for computing the QR factorisation of extremely ill-conditioned tall-and-skinny matrices on distributed memory systems. The algorithm is based on the communication-avoiding CholeskyQR2…
To effectively control large-scale distributed systems online, model predictive control (MPC) has to swiftly solve the underlying high-dimensional optimization. There are multiple techniques applied to accelerate the solving process in the…
CPU-GPU heterogeneous architectures are now commonly used in a wide variety of computing systems from mobile devices to supercomputers. Maximizing the throughput for multi-programmed workloads on such systems is indispensable as one single…
Many important real-world applications, such as System Identification with Gaussian Processes, involve solving linear systems with symmetric positive-definite matrices. The iterative CG method and direct solvers based on the Cholesky…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
Major chip manufacturers have all introduced multicore microprocessors. Multi-socket systems built from these processors are used for running various server applications. However to the best of our knowledge current commercial operating…