相关论文: TSM2X: High-Performance Tall-and-Skinny Matrix-Mat…
In recent years, mesh subdivision---the process of forging smooth free-form surfaces from coarse polygonal meshes---has become an indispensable production instrument. Although subdivision performance is crucial during simulation, animation…
Matrix-accelerated stencil computation is a hot research topic, yet its application to three-dimensional (3D) high-order stencils and HPC remains underexplored. With the emergence of matrix units on multicore CPUs, we analyze matrix-based…
The reduction of a banded matrix to bidiagonal form is a critical step in the calculation of Singular Values, a cornerstone of scientific computing and AI. Although inherently parallel, this step has traditionally been considered unsuitable…
Processing large-scale graph datasets is computationally intensive and time-consuming. Processor-centric CPU and GPU architectures, commonly used for graph applications, often face bottlenecks caused by extensive data movement between the…
The sizes of GPU applications are rapidly growing. They are exhausting the compute and memory resources of a single GPU, and are demanding the move to multiple GPUs. However, the performance of these applications scales sub-linearly with…
The Morse-Smale complex is a well studied topological structure that represents the gradient flow behavior between critical points of a scalar function. It supports multi-scale topological analysis and visualization of feature-rich…
We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The…
Many-particle continuous-time quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic…
Kronecker Matrix-Matrix Multiplication (Kron-Matmul) is the multiplication of a matrix with the Kronecker Product of several smaller matrices. Kron-Matmul is a core operation for many scientific and machine learning computations.…
Large language models~(LLMs) are known for their high demand on computing resources and memory due to their substantial model size, which leads to inefficient inference on moderate GPU systems. Techniques like quantization or pruning can…
The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a…
In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…
As users and developers, we are witnessing the opening of a new computing scenario: the introduction of hybrid processors into a single die, such as an accelerated processing unit (APU) processor, and the plug-and-play of additional…
A tridiagonal matrix algorithm (TDMA), Pipelined-TDMA, is developed for multi-GPU systems to resolve the scalability bottlenecks caused by the sequential structure of conventional divide-and-conquer TDMA. The proposed method pipelines…
Efficient high-performance libraries often expose multiple tunable parameters to provide highly optimized routines. These can range from simple loop unroll factors or vector sizes all the way to algorithmic changes, given that some…
Maximizing the performance potential of the modern day GPU architecture requires judicious utilization of available parallel resources. Although dramatic reductions can often be obtained through straightforward mappings, further performance…
The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Maker's Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such…
Graph neural networks (GNNs), an emerging deep learning model class, can extract meaningful representations from highly expressive graph-structured data and are therefore gaining popularity for wider ranges of applications. However, current…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
The resurgence of machine learning has increased the demand for high-performance basic linear algebra subroutines (BLAS), which have long depended on libraries to achieve peak performance on commodity hardware. High-performance BLAS…