Many scientific applications rely on sparse direct solvers for their numerical robustness. However, performance optimization for these solvers remains a challenging task, especially on GPUs. This is due to workloads of small dense matrices that are ...

This article describes a standard API for a set of Batched Basic Linear Algebra Subprograms (Batched BLAS or BBLAS). The focus is on many independent BLAS operations on small matrices that are grouped together and processed by a single routine, called a ...

Efficient processing of Irregular Matrices on Single Instruction, Multiple Data (SIMD)-type architectures is a persistent challenge. Resolving it requires innovations in the development of data formats, computational techniques, and implementations that ...

Low-precision floating-point arithmetic is a powerful tool for accelerating scientific computing applications, especially those in artificial intelligence. Here, we present an investigation showing that other high-performance computing (HPC) ...

Low-precision floating-point arithmetic is a powerful tool for accelerating scientific computing applications, especially those in artificial intelligence. Here, we present an investigation showing that other high-performance computing (HPC) ...

The use of low-precision arithmetic in mixed-precision computing methods has been a powerful tool to accelerate numerous scientific computing applications. Artificial intelligence (AI) in particular has pushed this to current extremes, making use of ...

This paper presents a software framework for solving large numbers of relatively small matrix problems using GPUs. Our approach combines novel and existing HPC techniques to methodically apply performance analysis, kernel design, low-level optimizations,...

We present our performance analysis, algorithm designs, and the optimizations needed for the development of high-performance GPU-only algorithms, and in particular, for the dense Cholesky factorization. In contrast to currently promoted designs that ...

In this paper we explore the performance portability of directives provided by OpenMP 4 and OpenACC to program various types of node architectures with attached accelerators, both self-hosted multicore and offload multicore/GPU. Our goal is to examine ...

Singular Value QR (SVQR) can orthonormalize a set of dense vectors with the minimum communication (one global reduction between the parallel processing units, and BLAS-3 to perform most of its local computation). As a result, compared to other ...

A wide variety of heterogeneous compute resources are available to modern computers, including multiple sockets containing multicore CPUs, one-or-more GPUs of varying power, and coprocessors such as the Intel Xeon Phi. The challenge faced by domain ...

We present a scalable implementation of the Linearized Augmented Plane Wave method for distributed memory systems, which relies on an efficient distributed, block-cyclic setup of the Hamiltonian and overlap matrices and allows us to turn around highly ...

The solution of nonsymmetric eigenvalue problems, A_x = λ_x, can be accelerated substantially by first reducing A to an upper Hessenberg matrix H that has the same eigenvalues as A. This can be done using Householder orthogonal transformations, which is a ...

This paper presents a heterogeneous CPU-GPU implementation for a sparse iterative eigensolver -- the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG). For the key routine generating the Krylov search spaces via the product of a sparse ...

As modern hardware keeps evolving, an increasingly effective approach to develop energy efficient and high-performance solvers is to design them to work on many small size independent problems. Many applications already need this functionality, ...

In this paper we unveil some energy efficiency and performance frontiers for sparse computations on GPU-based supercomputers. To do this, we consider state-of-the-art implementations of the sparse matrix-vector (SpMV) product in libraries like cuSPARSE, ...

As hardware evolves, an increasingly effective approach to develop energy efficient, high-performance solvers, is to design them to work on many small and independent problems. Indeed, many applications already need this functionality, especially for ...

The generalized minimum residual (GMRES) method is a popular method for solving a large-scale sparse nonsymmetric linear system of equations. On modern computers, especially on a large-scale system, the communication is becoming increasingly expensive. ...

Krylov subspace projection methods are widely used iterative methods for solving large-scale linear systems of equations. Researchers have demonstrated that communication-avoiding (CA) techniques can improve Krylov methods' performance on modern ...

This paper presents the design and implementation of several fundamental dense linear algebra (DLA) algorithms in OpenCL. In particular, these are linear system solvers and eigenvalue problem solvers. Further, we give an overview of the clMAGMA library, ...