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There is a stage in the GPU computing pipeline where a grid of thread-blocks is mapped to the problem domain. Normally, this grid is a k-dimensional bounding box that covers a k-dimensional problem no matter its shape. Threads that fall…
EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
Modern high-performance computing (HPC) increasingly relies on GPUs, but integrating GPU acceleration into complex scientific frameworks like OpenFOAM remains a challenge. Existing approaches either fully refactor the codebase or use…
As in various fields like scientific research and industrial application, the computation time optimization is becoming a task that is of increasing importance because of its highly parallel architecture. The graphics processing unit is…
We present a new implementation of the Floyd-Warshall All-Pairs Shortest Paths algorithm on CUDA. Our algorithm runs approximately 5 times faster than the previously best reported algorithm. In order to achieve this speedup, we applied a…
This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The…
Batched linear solvers play a vital role in computational sciences, especially in the fields of plasma physics and combustion simulations. With the imminent deployment of the Aurora Supercomputer and other upcoming systems equipped with…
In recent decades, High Performance Computing (HPC) has undergone significant enhancements, particularly in the realm of hardware platforms, aimed at delivering increased processing power while keeping power consumption within reasonable…
Matrix multiplication is fundamental in the backpropagation algorithm used to train deep neural network models. Libraries like Intel's MKL or NVIDIA's cuBLAS implemented new and optimized matrix multiplication techniques that increase…
The vision of super computer at every desk can be realized by powerful and highly parallel CPUs or GPUs or APUs. Graphics processors once specialized for the graphics applications only, are now used for the highly computational intensive…
We describe GPU implementations of the matrix recommender algorithms CCD++ and ALS. We compare the processing time and predictive ability of the GPU implementations with existing multi-core versions of the same algorithms. Results on the…
Transformer based Large Language Models (LLMs) have been widely used in many fields, and the efficiency of LLM inference becomes hot topic in real applications. However, LLMs are usually complicatedly designed in model structure with…
Graphics Processing Unit, or GPUs, have been successfully adopted both for graphic computation in 3D applications, and for general purpose application (GP-GPUs), thank to their tremendous performance-per-watt. Recently, there is a big…
The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse…
Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the…
On the GPU, hash table operation speed is determined in large part by cache line efficiency, and state-of-the-art hashing schemes thus divide tables into cache line-sized buckets. This raises the question whether performance can be further…
We introduce cuPDLPx, a further enhanced GPU-based first-order solver for linear programming. Building on the recently developed restarted Halpern PDHG for LP, cuPDLPx incorporates a number of new techniques, including a new restart…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…
Batch data analytics is a growing application for Large Language Models (LLMs). LLMs enable users to perform a wide range of natural language tasks, such as classification, entity extraction, and translation, over large datasets. However,…