Related papers: Fast Matrix Multiplication Without Tears: A Constr…
Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph structured linear systems, in the general setting, the bit complexity of solving an $n \times n$ linear…
This paper presents a new fast, highly scalable distributed matrix multiplication algorithm on Apache Spark, called Stark, based on Strassen's matrix multiplication algorithm. Stark preserves Strassen's 7 multiplications scheme in a…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
We show that assuming the availability of the processor with variable precision arithmetic, we can compute matrix-by-matrix multiplications in $O(N^2log_2N)$ computational complexity. We replace the standard matrix-by-matrix multiplications…
We study the Matrix Multiplication Verification Problem (MMV) where the goal is, given three $n \times n$ matrices $A$, $B$, and $C$ as input, to decide whether $AB = C$. A classic randomized algorithm by Freivalds (MFCS, 1979) solves MMV…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
Despite their tremendous success and versatility, Deep Neural Networks (DNNs) such as Large Language Models (LLMs) suffer from inference inefficiency and rely on advanced computational infrastructure. To address these challenges and make…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
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…
A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of segments needed…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…
In the Nonnegative Matrix Factorization (NMF) problem we are given an $n \times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n \times r$ and $r…
We study the problem of computing matrix chain multiplications in a distributed computing cluster. In such systems, performance is often limited by the straggler problem, where the slowest worker dominates the overall computation latency.…
Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time $O(n^{2.3755})$. Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le Gall has led to an…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
Constraint programming (CP) is a powerful tool for modeling mathematical concepts and objects and finding both solutions or counter examples. One of the major strengths of CP is that problems can easily be combined or expanded. In this…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
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,…