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Modern graphics computing units (GPUs) are designed and optimized to perform highly parallel numerical calculations. This parallelism has enabled (and promises) significant advantages, both in terms of energy performance and calculation. In…
This paper describes the application of the code generated by the CAMPARY software to accelerate the solving of linear systems in the least squares sense on Graphics Processing Units (GPUs), in double double, quad double, and octo double…
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…
GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have…
Tensor Core is a mixed-precision matrix-matrix multiplication unit on NVIDIA GPUs with a theoretical peak performance of more than 300 TFlop/s on Ampere architectures. Tensor Cores were developed in response to the high demand of dense…
Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
Fast Fourier Transform (FFT) is an essential tool in scientific and engineering computation. The increasing demand for mixed-precision FFT has made it possible to utilize half-precision floating-point (FP16) arithmetic for faster speed and…
The NVIDIA Volta GPU microarchitecture introduces a specialized unit, called "Tensor Core" that performs one matrix-multiply-and-accumulate on 4x4 matrices per clock cycle. The NVIDIA Tesla V100 accelerator, featuring the Volta…
Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput…
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving $\min_{E,r}…
Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming…
I present HPRMAT, a high-performance solver library for the linear systems arising in R-matrix coupled-channel scattering calculations in nuclear physics. Designed as a drop-in replacement for the linear algebra routines in existing…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
We investigate the use of half-precision floating-point numbers (FP16) in mixed-precision linear solvers for lattice QCD simulations. Since the emergence of GPUs for general-purpose, mixed-precision algorithms that combine single-precision…
The Nvidia GPU architecture has introduced new computing elements such as the \textit{tensor cores}, which are special processing units dedicated to perform fast matrix-multiply-accumulate (MMA) operations and accelerate \textit{Deep…
Efficient mixed-precision matrix multiply accumulate (MMA) operations are critical for accelerating deep learning workloads on GPGPUs. However, existing open-source dot product implementations for Tensor Cores rely on discrete arithmetic…