Related papers: Algorithms for matrix multiplication via sampling …
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world…
We consider the problem of reconstructing a rank-$k$ $n \times n$ matrix $M$ from a sampling of its entries. Under a certain incoherence assumption on $M$ and for the case when both the rank and the condition number of $M$ are bounded, it…
We consider the famous Strassen algorithm for fast multiplication of matrices. We show that this algorithm has a nontrivial finite group of automorphisms of order 36 (namely the direct product of two copies of the symmetric group on 3…
We give a new procedure in Maple for finding the k-th power of a martix. The algorithm is based on the article [1].
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…
This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…
We dispel with "street wisdom" regarding the practical implementation of Strassen's algorithm for matrix-matrix multiplication (DGEMM). Conventional wisdom: it is only practical for very large matrices. Our implementation is practical for…
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…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
The All-Pairs Shortest Paths (APSP) is a foundational problem in theoretical computer science. Approximating APSP in undirected unweighted graphs has been studied for many years, beginning with the work of Dor, Halperin and Zwick…
We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\in \mathbb{R}^{n\times m}$. RXTX uses $5\%$ fewer multiplications and $5\%$ fewer operations (additions and multiplications) than…
An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary ($\mathbb{Z}_2$), modular ternary ($\mathbb{Z}_3$) and…
We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…
Initiated by Mulmuley, Vazirani, and Vazirani (1987), many algebraic algorithms have been developed for matching and related problems. In this paper, we review basic facts and discuss possible improvements with the aid of fast computation…
The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
This work presents a new algorithm for matrix power series which is near-sparse, that is, there are a large number of near-zero elements in it. The proposed algorithm uses a filtering technique to improve the sparsity of the matrices…
We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…