Related papers: Time- and space-efficient evaluation of the comple…
A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density…
For a function of a type $ \left| \mathbf{r}_1{+}\ldots {+}\mathbf{r}_{_N} \right|^{-\nu} \in \mathbb{R} $ from the many-dimensional vectors $ \mathbf{r}_s $ in Euclidean space, the successive algebraic approach is the derivation of the…
We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally…
A new algorithm named EXPected Similarity Estimation (EXPoSE) was recently proposed to solve the problem of large-scale anomaly detection. It is a non-parametric and distribution free kernel method based on the Hilbert space embedding of…
The Multiplicative Weights Exponential Mechanism (MWEM) is a fundamental iterative framework for private data analysis, with broad applications such as answering $m$ linear queries, or privately solving systems of $m$ linear constraints.…
Two-time-scale stochastic approximation algorithms are iterative methods used in applications such as optimization, reinforcement learning, and control. Finite-time analysis of these algorithms has primarily focused on fixed point…
Evaluating solutions to optimization problems is arguably the most important step for heuristic algorithms, as it is used to guide the algorithms towards the optimal solution in the solution search space. Research has shown evaluation…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
We review the literature on algorithms for estimating the index space in a multi-index model. The primary focus is on computationally efficient (polynomial-time) algorithms in Gaussian space, the assumptions under which consistency is…
Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is…
We consider the problem of maximizing a monotone submodular function subject to a knapsack constraint. Our main contribution is an algorithm that achieves a nearly-optimal, $1 - 1/e - \epsilon$ approximation, using…
An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices.…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
An efficient method of computing power expansions of algebraic functions is the method of Kung and Traub and is based on exact arithmetic. This paper shows a numeric approach is both feasible and accurate while also introducing a…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…
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,…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
One-loop functions with loop masses larger than external masses and momenta can always be expanded in terms of external masses and momenta. The precision requested for observables determines the number of the expansion terms retained in the…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…