Related papers: Parallel Sparse Matrix Multiplication for Linear S…
Matrix multiplication is integral to various scientific and engineering disciplines, including machine learning, image processing, and gaming. With the increasing data volumes in areas like machine learning, the demand for efficient…
An efficient low-order scaling method is presented for large-scale electronic structure calculations based on the density functional theory using localized basis functions, which directly computes selected elements of the density matrix by…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…
Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…
Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…
Achieving high efficiency with numerical kernels for sparse matrices is of utmost importance, since they are part of many simulation codes and tend to use most of the available compute time and resources. In addition, especially in large…
Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct…
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
We evaluate optimized parallel sparse matrix-vector operations for two representative application areas on widespread multicore-based cluster configurations. First the single-socket baseline performance is analyzed and modeled with respect…
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…
A massively parallel order-N electronic structure theory was constructed by an interdisciplinary research between physics, applied mathematics and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on…
Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
We consider the problem of developing an efficient multi-threaded implementation of the matrix-vector multiplication algorithm for sparse matrices with structural symmetry. Matrices are stored using the compressed sparse row-column format…
The increasing importance of multicore processors calls for a reevaluation of established numerical algorithms in view of their ability to profit from this new hardware concept. In order to optimize the existent algorithms, a detailed…