Related papers: GBLA -- Gr\"obner Basis Linear Algebra Package

Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core…

Processors with large numbers of cores are becoming commonplace. In order to take advantage of the available resources in these systems, the programming paradigm has to move towards increased parallelism. However, increasing the level of…

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel…

Faugere's F5 algorithm computes a Groebner basis incrementally, by computing a sequence of (non-reduced) Groebner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Groebner basis with its reduced…

Past decade has seen the development of many shared-memory graph processing frameworks, intended to reduce the effort of developing high performance parallel applications. However many of these frameworks, based on Vertex-centric or…

Reduction operations are extensively employed in many computational problems. A reduction consists of, given a finite set of numeric elements, combining into a single value all elements in that set, using for this a combiner function. A…

This paper is a survey on the area of signature-based Gr\"obner basis algorithms that was initiated by Faug\`ere's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the various known…

Usage of GPUs as co-processors is a well-established approach to accelerate costly algorithms operating on matrices and vectors. We aim to further improve the performance of the Global Neutrino Analysis framework (GNA) by adding GPU support…

We present GLB, a programming model and an associated implementation that can handle a wide range of irregular paral- lel programming problems running over large-scale distributed systems. GLB is applicable both to problems that are easily…

Recent advances in graph learning have paved the way for innovative retrieval-augmented generation (RAG) systems that leverage the inherent relational structures in graph data. However, many existing approaches suffer from rigid, fixed…

This paper advocates for an intertwined design of the dense linear algebra software stack that breaks down the strict barriers between the high-level, blocked algorithms in LAPACK (Linear Algebra PACKage) and the low-level,…

Basic Linear Algebra Subprograms (BLAS) play key role in high performance and scientific computing applications. Experimentally, yesteryear multicore and General Purpose Graphics Processing Units (GPGPUs) are capable of achieving up to 15…

Modern GPUs are able to perform significantly more arithmetic operations than transfers of a single word to or from global memory. Hence, many GPU kernels are limited by memory bandwidth and cannot exploit the arithmetic power of GPUs.…

Linear algebra routines are basic building blocks for the statistical software. In this paper we analyzed how can we can improve R performance for matrix computations. We benchmarked few matrix operations using the standard linear algebra…

Extensive prior research has focused on alleviating the characteristic poor cache locality of graph analytics workloads. However, graph pre-processing tasks remain relatively unexplored. In many important scenarios, graph pre-processing…

The rapid development of large language models (LLM) has greatly enhanced everyday applications. While many FPGA-based accelerators, with flexibility for fine-grained data control, exhibit superior speed and energy efficiency compared to…

Solving zero-dimensional polynomial systems using Gr\"obner bases is usually done by, first, computing a Gr\"obner basis for the degree reverse lexicographic order, and next computing the lexicographic Gr\"obner basis with a change of order…

In cloud machine learning (ML) inference systems, providing low latency to end-users is of utmost importance. However, maximizing server utilization and system throughput is also crucial for ML service providers as it helps lower the…

Training Large Language Models (LLMs) presents significant memory challenges, predominantly due to the growing size of weights and optimizer states. Common memory-reduction approaches, such as low-rank adaptation (LoRA), add a trainable…

Scientific programmers often turn to vendor-tuned Basic Linear Algebra Subprograms (BLAS) to obtain portable high performance. However, many numerical algorithms require several BLAS calls in sequence, and those successive calls result in…