Related papers: On fast matrix-vector multiplication with a Hankel…
This paper proposes a class of power-of-two FFT (Fast Fourier Transform) algorithms, called AM-QFT algorithms, that contains the improved QFT (Quick Fourier Transform), an algorithm recently published, as a special case. The main idea is to…
Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with 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…
On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to…
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a…
Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes whose coefficients are restricted to the set $\{-1, 0, 1\}$…
In this paper, a new method to compute a B\'ezier curve of degree n = 2m-1 is introduced, here formulated as a set of points whose coordinates are calculated from two Hankel forms in $\C^m$. From Vandermonde factorizations of the two…
In this work the algorithms of fast multiplication of matrices are considered. To any algorithm there associated a certain group of automorphisms. These automorphism groups are found for some well-known algorithms, including algorithms of…
Floating point multiplication is a crucial operation in high power computing applications such as image processing, signal processing etc. And also multiplication is the most time and power consuming operation. This paper proposes an…
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learning-based algorithm…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We use lookup tables to design faster algorithms for important algebraic problems over finite fields. These faster algorithms, which only use arithmetic operations and lookup table operations, may help to explain the difficulty of…
We present a new, simple, and efficient approach for computing the Lempel-Ziv (LZ77) factorization of a string in linear time, based on suffix arrays. Computational experiments on various data sets show that our approach constantly…
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…
While the Karatsuba algorithm reduces the complexity of large integer multiplication, the extra additions required minimize its benefits for smaller integers of more commonly-used bitwidths. In this work, we propose the extension of the…
OpenTensor is a reproduction of AlphaTensor, which discovered a new algorithm that outperforms the state-of-the-art methods for matrix multiplication by Deep Reinforcement Learning (DRL). While AlphaTensor provides a promising framework for…
Recent advancements have illuminated the efficacy of some tensorization-decomposition Parameter-Efficient Fine-Tuning methods like LoRA and FacT in the context of Vision Transformers (ViT). However, these methods grapple with the challenges…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…