Related papers: Randomization of Approximate Bilinear Computation …
Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not…
Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…
The goal of Boolean Matrix Factorization (BMF) is to approximate a given binary matrix as the product of two low-rank binary factor matrices, where the product of the factor matrices is computed under the Boolean algebra. While the problem…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of…
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,…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We study applications of clustering (in particular, the $k$-center clustering problem) in the design of efficient and practical algorithms for computing an approximate and the exact arithmetic matrix product of two 0-1 rectangular matrices…
An algorithm for matrix factorization of polynomials was proposed in \cite{fomatati2022tensor} and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible…
We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are…
We study the top Lyapunov exponents of random products of positive $2 \times 2$ matrices and obtain an efficient algorithm for its computation. As in the earlier work of Pollicott, the algorithm is based on the Fredholm theory of…
Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…