Related papers: Matrix Multiplication Using Only Addition
Matrix-multiply-accumulate (MMA) units, or tensor cores, are now widespread across modern computing architectures. Yet, their use for particle-grid operators remains limited. In implicit particle methods, mass-matrix assembly is a…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
Although the matrix multiplication plays a vital role in computational linear algebra, there are few efficient solutions for matrix multiplication of the near-sparse matrices. The Sparse Approximate Matrix Multiply (SpAMM) is one of the…
In this paper we present a hardware-oriented algorithm for constant matrix-vector product calculating, when the all elements of vector and matrix are complex numbers. The proposed algorithm versus the naive method of analogous calculations…
We investigate effects of ordering in blocked matrix--matrix multiplication. We find that submatrices do not have to be stored contiguously in memory to achieve near optimal performance. Instead it is the choice of execution order of the…
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer…
We present a non-commutative algorithm for multiplying (7x7) matrices using 250 multiplications and a non-commutative algorithm for multiplying (9x9) matrices using 520 multiplications. These algorithms are obtained using the same…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
The paper presents the aspect of use of modern graphics accelerators supporting CUDA technology for high-performance computing in the field of linear algebra. Fully programmable graphic cards have been available for several years for both…
In-memory computing hardware accelerators allow more than 10x improvements in peak efficiency and performance for matrix-vector multiplications (MVM) compared to conventional digital designs. For this, they have gained great interest for…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
This paper proposes four quadrant analog multiplier using CMOS-memristor circuit. Currently, there are plenty of analog multipliers using resistors and CMOS transistors. They can attain perfect multiplication but have several disadvantages…
The increasing complexity of transformer models in artificial intelligence expands their computational costs, memory usage, and energy consumption. Hardware acceleration tackles the ensuing challenges by designing processors and…
Multiplication is a fundamental operation in many applications, and multipliers are widely adopted in various circuits. However, optimizing multipliers is challenging due to the extensive design space. In this paper, we propose a multiplier…
Large-scale programmable photonic circuits are opening up new possibilities for information processing providing fast and energy-efficient means for matrix-vector multiplication. Here, we introduce a novel architecture of photonic circuits…
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…
Optical and optoelectronic approaches of performing matrix-vector multiplication (MVM) operations have shown the great promise of accelerating machine learning (ML) algorithms with unprecedented performance. The incorporation of…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
Consecutive matrix multiplications are commonly used in graph neural networks and sparse linear solvers. These operations frequently access the same matrices for both reading and writing. While reusing these matrices improves data locality,…