Related papers: Hierarchical Precision and Recursion for Accelerat…
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…
For a linear matrix function $f$ in $X \in \R^{m\times n}$ we consider inhomogeneous linear matrix equations $f(X) = E$ for $E \neq 0$ that have or do not have solutions. For such systems we compute optimal norm constrained solutions…
In this paper, we consider two fundamental symmetric kernels in linear algebra: the Cholesky factorization and the symmetric rank-$k$ update (SYRK), with the classical three nested loops algorithms for these kernels. In addition, we…
The functional renormalisation group (fRG) has evolved into a versatile tool in condensed matter theory for studying important aspects of correlated electron systems. Practical applications of the method often involve a high numerical…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
The simulation of turbulence in the boundary region of a tokamak is crucial for understanding and optimizing the performance of fusion reactors. In this work, the use of low-rank linear algebra techniques is shown to enhance the efficiency…
We introduce a fusion of GPU accelerated primal heuristics for Mixed Integer Programming. Leveraging GPU acceleration enables exploration of larger search regions and faster iterations. A GPU-accelerated PDLP serves as an approximate LP…
AcceleratedKernels.jl is introduced as a backend-agnostic library for parallel computing in Julia, natively targeting NVIDIA, AMD, Intel, and Apple accelerators via a unique transpilation architecture. Written in a unified, compact…
Genomic sequence alignment is an important research topic in bioinformatics and continues to attract significant efforts. As genomic data grow exponentially, however, most of alignment methods face challenges due to their huge computational…
We introduce a new algorithm and software for solving linear equations in symmetric diagonally dominant matrices with non-positive off-diagonal entries (SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate gradient…
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…
We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the…
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…
In this paper, we explore the acceleration of tensor product operations in finite element methods, leveraging the computational power of the NVIDIA A100 GPU Tensor Cores. We provide an accessible overview of the necessary mathematical…
LLM-based Triton kernel generation has attracted significant interest, yet a fundamental empirical question remains unanswered: where does this capability break down, and why? We present KernelBenchX, a benchmark designed to answer this…
We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
With the push towards Exascale computing and data-driven methods, problem sizes have increased dramatically, increasing the computational requirements of the underlying algorithms. This has led to a push to offload computations to general…
Mixed-precision neural network (MPNN) that utilizes just enough data width for the neural network processing is an effective approach to meet the stringent resources constraints including memory and computing of MCUs. Nevertheless, there is…