Related papers: A non-commutative algorithm for multiplying 5x5 ma…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer…
We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…
We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers $p$ and $q$ in base $pq$ to higher dimensional multiplication tessellation systems. We develop the theory of these…
Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
Several efficient distributed algorithms have been developed for matrix-matrix multiplication: the 3D algorithm, the 2D SUMMA algorithm, and the 2.5D algorithm. Each of these algorithms was independently conceived and they trade-off memory…
Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…
We propose and analyze a compact and non-volatile nanomagnetic (all-spin) non-binary matrix multiplier performing the multiply-and-accumulate (MAC) operation using two magnetic tunnel junctions - one activated by strain to act as the…
The online Markov decision process (MDP) is a generalization of the classical Markov decision process that incorporates changing reward functions. In this paper, we propose practical online MDP algorithms with policy iteration and…
Using three coupled harmonic oscillators, we present an amplitude-amplification method for factorization of an integer. We generalize the method in [arXiv:1007.4338] by employing non-orthogonal measurements on the harmonic oscillator. This…
Nowadays computational complexity of fast walsh hadamard transform and nonlinearity for Boolean functions and large substitution boxes is a major challenge of modern cryptography research on strengthening encryption schemes against linear…
Higher-order Markov chains play a very important role in many fields, ranging from multilinear PageRank to financial modeling. In this paper, we propose three accelerated higher-order power methods for computing the limiting probability…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
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.
This article is concerned with the efficient computation of modular matrix multiplication C=AB mod p, a key kernel in computer algebra. We focus on floating-point arithmetic, which allows for using efficient matrix multiplication libraries.…