Related papers: Matrix Multiplication Using Only Addition
Computing-in-Memory (CIM) accelerators are a promising solution for accelerating Machine Learning (ML) workloads, as they perform Matrix-Vector Multiplications (MVMs) on crossbar arrays directly in memory. Although the bit widths of the…
Matrix-accelerated stencil computation is a hot research topic, yet its application to three-dimensional (3D) high-order stencils and HPC remains underexplored. With the emergence of matrix units on multicore CPUs, we analyze matrix-based…
Processors may find some elementary operations to be faster than the others. Although an operation may be conceptually as simple as some other operation, the processing speeds of the two can vary. A clever programmer will always try to…
We propose several new schedules for Strassen-Winograd's matrix multiplication algorithm, they reduce the extra memory allocation requirements by three different means: by introducing a few pre-additions, by overwriting the input matrices,…
We show that the product of an nx3 matrix and a 3x3 matrix over a commutative ring can be computed using 6n+3 multiplications. For two 3x3 matrices this gives us an algorithm using 21 multiplications. This is an improvement with respect to…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
Images typically are represented as uniformly sampled data in the form of matrix of pixels/voxels. Therefore, matrix multiply-and-accumulate (MAC) forms the core of most state-of-the-art image analysis algorithms. While digital…
Matrix computation is ubiquitous in modern scientific and engineering fields. Due to the high computational complexity in conventional digital computers, matrix computation represents a heavy workload in many data-intensive applications,…
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.…
We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings $\Zb/m\Zb$. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve…
Multilevel/multigrid methods is one of the most popular approaches for solving a large sparse linear system of equations, typically, arising from the discretization of partial differential equations. One critical step in the…
Quantum circuits which perform integer arithmetic could potentially outperform their classical counterparts. In this paper, a quantum circuit is considered which performs a specific computational pattern on classically represented integers…
One of the most common, but at the same time expensive operations in linear algebra, is multiplying two matrices $A$ and $B$. With the rapid development of machine learning and increases in data volume, performing fast matrix intensive…
Sparse tensor computing is a core computational part of numerous applications in areas such as data science, graph processing, and scientific computing. Sparse tensors offer the potential of skipping unnecessary computations caused by zero…
Quantum multiplication is a fundamental operation in quantum computing. It is important to have a quantum multiplier with low complexity. In this paper, we propose the Quantum Multiplier Based on Exponent Adder (QMbead), a new approach that…
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…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
Fast matrix multiplication algorithms may be useful, provided that their running time is good in practice. Particularly, the leading coefficient of their arithmetic complexity needs to be small. Many sub-cubic algorithms have large leading…
High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…
The computing paradigm invented for processing a small amount of data on a single segregated processor cannot meet the challenges set by the present-day computing demands. The paper proposes a new computing paradigm (extending the old one…