Related papers: Faster Rectangular Matrix Multiplication by Combin…
We describe certain special consequences of certain elementary methods from group theory for studying the algebraic complexity of matrix multiplication, as developed by H. Cohn, C. Umans et. al. in 2003 and 2005. The measure of complexity…
We propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves the 18th order of convergence by using only seven matrix multiplication per iteration loop. This is the record high…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
Obeying constraints imposed by classical physics, we give optimal fine-grained algorithms for matrix multiplication and problems involving graphs and mazes, where all calculations are done in 3-dimensional space. We assume that whatever the…
In the manufacturing process of a filler-reinforced composite, the fillers in the matrix are aligned due to the shear flow occurring during the drawing stage, and the interface between the matrix and the fillers form various imperfections…
Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present here improved rank bounds for about thirty matrix formats.
A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by $n$, the algorithm uses $O(n^{1.43})$ field operations, breaking…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
An estimated state-space model can possibly be improved by further iterations with estimation data. This contribution specifically studies if models obtained by subspace estimation can be improved by subsequent re-estimation of the B, C,…
One of the most famous conjectures in computer algebra is that matrix multiplication might be feasible in not much more than quadratic time. The best known exponent is 2.376, due to Coppersmith and Winograd. Many attempts to solve this…
The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log 2 (7) $\approx$ 2.8074.…
We study the growth rate of the hard squares lattice gas, equivalent to the number of independent sets on the square lattice, and two related models - non-attacking kings and read-write isolated memory. We use an assortment of techniques…
Min-plus product of two $n\times n$ matrices is a fundamental problem in algorithm research. It is known to be equivalent to APSP, and in general it has no truly subcubic algorithms. In this paper, we focus on the min-plus product on a…
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…
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…
Canonical polyadic decomposition (CPD) is at the core of fast matrix multiplication, a computational problem with widespread implications across several seemingly unrelated problems in computer science. Much recent progress in this field…
In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an…
We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, or monomial algebras. We analyse them using Strassen's laser method and obtain an upper bound $2.431$ on $\omega$. We also…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…