Related papers: Witnessing a Poincar\'e recurrence with Mathematic…
Hundred twenty years after the fundamental work of Poincar\'e, the statistics of Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom is studied by numerical simulations. The obtained results show that in a regime,…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
This article is about both approximation theory and the numerical solution of partial differential equations (PDEs). First we introduce the notion of {\em reciprocal-log} or {\em log-lightning approximation} of analytic functions with…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
This paper provides a numerical approach for solving the linear stochastic Volterra integral equation using Walsh function approximation and the corresponding operational matrix of integration. A convergence analysis and error analysis of…
It has previously been shown that by using reinforcement learning (RL), agents can derive simple approximate and exact-restricted numeral systems that are similar to human ones (Carlsson, 2021). However, it is a major challenge to show how…
Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…
We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the…
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are…
The resampling algorithm of Moser \& Tardos is a powerful approach to develop constructive versions of the Lov\'{a}sz Local Lemma (LLL). We generalize this to partial resampling: when a bad event holds, we resample an appropriately-random…
We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations…
Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process,…
We consider a family of nonlinear recurrences with the Laurent property. Although these recurrences are not generated by mutations in a cluster algebra, they fit within the broader framework of Laurent phenomenon algebras, as introduced…
Given a convex function $f$ on $\mathbb{R}^n$ with an integer minimizer, we show how to find an exact minimizer of $f$ using $O(n^2 \log n)$ calls to a separation oracle and $O(n^4 \log n)$ time. The previous best polynomial time algorithm…
While there has been significant progress on algorithmic aspects of the Lov\'{a}sz Local Lemma (LLL) in recent years, a noteworthy exception is when the LLL is used in the context of random permutations. The breakthrough algorithm of Moser…
Solution of the discretized Lippmann-Schwinger equation in the spatial frequency domain involves the inversion of a linear operator specified by the scattering potential. To regularize this inevitably ill-conditioned problem, we propose a…