Related papers: New ways to multiply 3 x 3-matrices

Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous…

This paper considers the problem of calculating the matrix multiplication of two massive matrices $\mathbf{A}$ and $\mathbf{B}$ distributedly. We provide a modulo technique that can be applied to coded distributed matrix multiplication…

For $n>3$, every $n\times n$ partial Cayley matrix with at most $n-1$ holes can be reconstructed by quadrangle criterion. Moreover, the holes can be filled in given order. Without additional assumptions, this is the best possible result.…

We present a non-commutative algorithm for the multiplication of a 2 x 2 block-matrix by its adjoint, defined by a matrix ring anti-homomorphism. This algorithm uses 5 block products (3 recursive calls and 2 general products)over C or in…

In this work a rationalized algorithm for calculating the quotient of two complex numbers is presented which reduces the number of underlying real multiplications. The performing of a complex number division using the naive method takes 4…

We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.

We present a necessary and sufficient condition for a 3 by 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 by 3 matrix can be tested. This test generalizes to a…

We propose several new schedules for Strassen-Winograd's matrix multiplication algorithm, they reduce the extra memory allocation requirements by three different means: by introducing a few pre-additions, by overwriting the input matrices,…

We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…

The (asymptotic) complexity of matrix multiplication (over the complex field) is measured by a real parameter w > 0, called the exponent of matrix multiplication (over the complex field), which is defined to be the smallest real number w >…

In this study, we propose a simple method for fault-tolerant Strassen-like matrix multiplications. The proposed method is based on using two distinct Strassen-like algorithms instead of replicating a given one. We have realized that using…

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 $\{-1, 0, 1\}$…

We propose a non-commutative algorithm for multiplying 2x2 matrices using 7 coefficient products. This algorithm reaches simultaneously a better accuracy in practice compared to previously known such fast algorithms, and a time complexity…

In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…

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,…

In the past 20 years, compactifications of the families of curves in algebraic varieties X have been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable quotients. Each path leads to a different enumeration…

We present a new construction of triple arrays by combining a symmetric 2-design with a resolution of another 2-design. This is the first general method capable of producing non-extremal triple arrays. We call the triple arrays which can be…

We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…

We study the algorithmic problem of multiplying large matrices that are rectangular. We prove that the method that has been used to construct the fastest algorithms for rectangular matrix multiplication cannot give algorithms with…

Triangular numbers that are multiple of other triangular numbers are investigated. It is known that for any positive non-square integer multiplier, there is an infinity of multiples of triangular numbers which are triangular numbers. If the…