Related papers: An Algorithm for Computing Coefficients of Words i…

This paper provides an algebraic framework for the generation of order conditions for the construction of exponential integrators like splitting and Magnus-type methods for the numerical solution of evolution equations. The generation of…

We present an analysis based on word combinatorics of splitting integrators for Ito or Stratonovich systems of stochastic differential equations. In particular we present a technique to write down systematically the expansion of the local…

We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…

A systematic algorithm for building integrating factors of the form mu(x,y), mu(x,y') or mu(y,y') for second order ODEs is presented. The algorithm can determine the existence and explicit form of the integrating factors themselves without…

The purpose of this paper is to present a recursive algorithm and its implementation in Maple and Mathematica for the computation of joint moments and cumulants of Hawkes processes with exponential kernels. Numerical results and computation…

Uncontextualized word embeddings are reliable feature representations of words used to obtain high quality results for various NLP applications. Given the historical success of word embeddings in NLP, we propose a retrospective on some of…

A systematic algorithm for building integrating factors of the form mu(x,y') or mu(y,y') for non-linear second order ODEs is presented. When such an integrating factor exists, the algorithm determines it without solving any differential…

This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be…

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…

Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…

We present a program for the reduction of large systems of integrals to master integrals. The algorithm was first proposed by Laporta; in this paper, we implement it in MAPLE. We also develop two new features which keep the size of…

Natural language processing (NLP) models often require a massive number of parameters for word embeddings, resulting in a large storage or memory footprint. Deploying neural NLP models to mobile devices requires compressing the word…

This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the setup of a system of order conditions for operator splitting…

In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…

In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the…

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra…

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…

Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…

We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…

We present a technique, based on so-called word series, to write down in a systematic way expansions of the strong and weak local errors of splitting algorithms for the integration of Stratonovich stochastic differential equations. Those…