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A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
Finite field multiplier is mainly used in error-correcting codes and signal processing. Finite field multiplier is regarded as the bottleneck arithmetic unit for such applications and it is the most complicated operation over finite field…
This paper describes a regularized variant of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex programs. It is shown that the pointwise iteration-complexity of the new method is better than the…
Modern Neural Network (NN) architectures heavily rely on vast numbers of multiply-accumulate arithmetic operations, constituting the predominant computational cost. Therefore, this paper proposes a high-throughput, scalable and energy…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Computational memory (CM) is a promising approach for accelerating inference on neural networks (NN) by using enhanced memories that, in addition to storing data, allow computations on them. One of the main challenges of this approach is…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…
We present an optimized algorithm calculating determinant for multivariate polynomial matrix on GPU. The novel algorithm provides precise determinant for input multivariate polynomial matrix in controllable time. Our approach is based on…
This article presents a vertical multiplication formula for calculating the multiplication of any two multi-digit integers, which may be not only used to design the multiplier but also to the mental multiplication. Our algorithm is a…
In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…
In this paper, we propose and study a fast multilevel dimension iteration (MDI) algorithm for computing arbitrary $d$-dimensional integrals based on tensor product approximations. It reduces the computational complexity (in terms of the CPU…
This paper will describe a simulator developed by the authors to explore the design of Fourier transform based multiplication using optics. Then it will demonstrate an application to the problem of constructing an all-optical modular…
This paper deals with circulant matrices. It is shown that a circulant matrix can be multiplied by a vector in time O(n log(n)) in a ring with roots of unity without making use of an FFT algorithm. With our algorithm we achieve a speedup of…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
We present new algorithms for computing the low $n$ bits or the high $n$ bits of the product of two $n$-bit integers. We show that these problems may be solved in asymptotically 75% of the time required to compute the full $2n$-bit product,…
This article presents new properties of the mesh array for matrix multiplication. In contrast to the standard array that requires 3n-2 steps to complete its computation, the mesh array requires only 2n-1 steps. Symmetries of the mesh array…
The performance of deep learning algorithms such as neural networks (NNs) has increased tremendously recently, and they can achieve state-of-the-art performance in many domains. However, due to memory and computation resource constraints,…
We present an efficient algorithm to multiply two hyperbolic octonions. The direct multiplication of two hyperbolic octonions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how…
We study the problem of multiplying two bit matrices with entries either over the Boolean algebra $(0,1,\vee,\wedge)$ or over the binary field $(0,1,+,\cdot)$. We engineer high-performance open-source algorithm implementations for…