Related papers: Reduction systems and degree bounds for integratio…
The construction of the general solution sequence of row-finite linear systems is accomplished by implementing -ad infinitum- the Gauss-Jordan algorithm under a rightmost pivot elimination strategy. The algorithm generates a basis (finite…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with…
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we…
Numerical integration (NI) packages commonly used in scientific research are limited to returning the value of a definite integral at the upper integration limit, also commonly referred to as numerical quadrature. These quadrature…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…
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…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
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…
This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…
Greedy point insertion algorithms have emerged as an attractive tool for the solution of minimization problems over the space of Radon measures. Conceptually, these methods can be split into two phases: first, the computation of a new…
We construct non-compactness examples for the fully coupled Einstein-Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional…
We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…
We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In opposition to the popular approach with projection methods,…
For an algebraic number $\alpha$ we consider the orders of the reductions of $\alpha$ in finite fields. In the case where $\alpha$ is an integer, it is known by the work on Artin's primitive root conjecture that the order is "almost always…