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Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…
We study distributed computing of the truncated singular value decomposition problem. We develop an algorithm that we call \texttt{LocalPower} for improving communication efficiency. Specifically, we uniformly partition the dataset among…
In this paper, we develop new algorithms for the basic RNA folding problem. Given an RNA sequence that contains $n$ nucleotides, the goal of the problem is to compute a pseudoknot-free secondary structure that maximizes the number of base…
We develop an extension of recently developed methods for obtaining time-space tradeoff lower bounds for problems of learning from random test samples to handle the situation where the space of tests is signficantly smaller than the space…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
A rigorous convergence analysis of the Strang splitting algorithm with a discontinuous Galerkin approximation in space for the Vlasov--Poisson equations is provided. It is shown that under suitable assumptions the error is of order…
We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
We present a new algorithm for Tukey (halfspace) depth level sets and its implementation. Given $d$-dimensional data set for any $d\geq 2$, the algorithm is based on representation of level sets as intersections of balls in $R^d$, and can…
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to…
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to…
Almost everywhere convergence on the solution of Schr\"odinger equation is an important problem raised by Carleson in harmonic analysis. In recent years, this problem was essentially solved by building the sharp $L^p$-estimate of…
The problem of recovering partial derivatives of high orders of bivariate functions with finite smoothness is studied. Based on the truncation method, a numerical differentiation algorithm was constructed, which is optimal by the order,…
Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an $n$-variate polynomial with bounded individual degree $d$ and…
Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…
We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an…
Recently, Sidford, Wang, Wu and Ye (2018) developed an algorithm combining variance reduction techniques with value iteration to solve discounted Markov decision processes. This algorithm has a sublinear complexity when the discount factor…
Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…