Related papers: A dynamical algorithm to compute hyperbolic Julia …
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software…
The perceptron algorithm for linear programming, arising from machine learning, has been around since the 1950s. While not a polynomial-time algorithm, it is useful in practice due to its simplicity and robustness. In 2004, Dunagan and…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…
The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend…
Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…
Applying parallel-in-time algorithms to multiscale Hamiltonian systems to obtain stable long time simulations is very challenging. In this paper, we present novel data-driven methods aimed at improving the standard parareal algorithm…
Sequential Latin hypercube designs have recently received great attention for computer experiments. Much of the work has been restricted to invariant spaces. The related systematic construction methods are inflexible while algorithmic…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a "post-processing algorithm", checking that…
We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…
In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…
The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then…
The automaton constrained tree knapsack problem is a variant of the knapsack problem in which the items are associated with the vertices of the tree, and we can select a subset of items that is accepted by a top-down tree automaton. If the…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…