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We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…

Modeling data sharing in GPU programs is a challenging task because of the massive parallelism and complex data sharing patterns provided by GPU architectures. Better GPU caching efficiency can be achieved through careful task scheduling…

Sparse Matrix-Vector Multiplication (SpMV) is the cornerstone in many iterative workloads, including large-scale graph analytics and sparse iterative solvers. Accelerating SpMV on real-world graphs remains challenging due to highly…

B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these…

We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…

We propose a novel approach which employs random sampling to generate an accurate non-uniform mesh for numerically solving Partial Differential Equation Boundary Value Problems (PDE-BVP's). From a uniform probability distribution U over a…

In this paper we solve on GPUs massive problems with large amount of data, which are not appropriate for solution with the SIMD technology. For the given problem we consider a three-level parallelization. The multithreading of CPU is used…

This paper introduces CKTSO (abbreviation of "circuit solver"), a novel sparse linear solver specially designed for the simulation program with integrated circuit emphasis (SPICE). CKTSO is a parallel solver and can be run on a multi-core,…

A novel parallelization paradigm has been developed for multi-GPU architectures. Classical multi-GPU parallelization for SPH rely on domain decomposition. In our approach each particle can be assigned to a GPU independently of its position…

The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…

As neural network model sizes have dramatically increased, so has the interest in various techniques to reduce their parameter counts and accelerate their execution. An active area of research in this field is sparsity - encouraging zero…

We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…

Partitioning sparse matrices and graphs is a common and important problem in many scientific and graph analytics applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as…

Matrix Factorization (MF) on large scale data takes substantial time on a Central Processing Unit (CPU). While Graphical Processing Unit (GPU)s could expedite the computation of MF, the available memory on a GPU is finite. Leveraging GPUs…

We describe a simple algorithm for spectral graph sparsification, based on iterative computations of weighted spanners and uniform sampling. Leveraging the algorithms of Baswana and Sen for computing spanners, we obtain the first…

Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…

Designing efficient and scalable sparse linear algebra kernels on modern multi-GPU based HPC systems is a daunting task due to significant irregular memory references and workload imbalance across the GPUs. This is particularly the case for…

To enhance the efficiency, scalability, and cross-survey applicability of stellar parameter inference in large spectroscopic datasets, we present a modular, parallelized Python framework with automated error estimation, built on the LAMOST…

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…

In this paper, we show the effectiveness of a pipeline implementation of Dynamic Programming (DP) on GPU. As an example, we explain how to solve a matrix-chain multiplication (MCM) problem by DP on GPU. This problem can be sequentially…