Related papers: HYLU: Hybrid Parallel Sparse LU Factorization
In this paper, we consider the matrices approximated in H2 format. The direct solution, as well as the preconditioning, of systems with such matrices is a challenging problem. We propose a non-extensive sparse factorization of the H2 matrix…
Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…
High-level synthesis (HLS) has enabled the rapid development of custom hardware circuits for many software applications. However, developing high-performance hardware circuits using HLS is still a non-trivial task requiring expertise in…
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed multi-core nodes. These platforms make the present and the foreseeable future of…
This paper provides a theoretical framework on the solution of feedforward ReLU networks for interpolations, in terms of what is called an interpolation matrix, which is the summary, extension and generalization of our three preceding…
Polyhedral optimisation, a methodology that views nested loops as polyhedra and searches for their optimal transformation regarding specific objectives (parallelism, locality, etc.), sounds promising for mitigating difficulties in…
The significant resource demands in LLM serving prompts production clusters to fully utilize heterogeneous hardware by partitioning LLM models across a mix of high-end and low-end GPUs. However, existing parallelization approaches often…
Emerging analog computing substrates, such as oscillator-based Ising machines, offer rapid convergence times for combinatorial optimization but often suffer from limited scalability due to physical implementation constraints. To tackle…
We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of…
Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) $V$-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has…
Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…
Hardware development critically depends on cycle-accurate RTL simulation. However, as chip complexity increases, conventional single-threaded simulation becomes impractical due to stagnant single-core performance. Parendi is an RTL…
Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across $k$ different blocks of bounded size, such that…
Many important real-world applications, such as System Identification with Gaussian Processes, involve solving linear systems with symmetric positive-definite matrices. The iterative CG method and direct solvers based on the Cholesky…
Large language models (LLMs) deliver impressive performance but incur prohibitive memory and compute costs at deployment. Model pruning is an effective way to reduce these overheads, yet existing approaches face challenges: unstructured…
There has been significant progress in the development of quantum algorithms for solving linear systems of equations with a growing body of applications to Computational Fluid Dynamics (CFD) and CFD-like problems. This work extends previous…
Long-context inference in Large Language Models (LLMs) is bottlenecked by the quadratic computation complexity of attention and the substantial memory footprint of Key-Value (KV) caches. While existing sparse attention mechanisms attempt to…
We present Cyqlone, a solver for linear systems with a stage-wise optimal control structure that fully exploits the various levels of parallelism available in modern hardware. Cyqlone unifies algorithms based on the sequential Riccati…