Related papers: Lazy Hermite Reduction and Creative Telescoping fo…
Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite…
Continuing a series of articles in the past few years on creative telescoping using reductions, we develop a new algorithm to construct minimal telescopers for algebraic functions. This algorithm is based on Trager's Hermite reduction and…
Continuing a series of articles in the past few years on creative telescoping using reductions, we adapt Trager's Hermite reduction for algebraic functions to fuchsian D-finite functions and develop a reduction-based creative telescoping…
Trager's Hermite reduction solves the integration problem for algebraic functions via integral bases. A generalization of this algorithm to D-finite functions has so far been limited to the Fuchsian case. In the present paper, we remove…
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain…
We present a reduction algorithm that simultaneously extends Hermite's reduction for rational functions and the Hermite-like reduction for hyperexponential functions. It yields a unique additive decomposition and allows to decide…
Creative telescoping is a powerful computer algebra paradigm -initiated by Doron Zeilberger in the 90's- for dealing with definite integrals and sums with parameters. We address the mixed continuous-discrete case, and focus on the…
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite…
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest…
We introduce a method for computing some pseudo-elliptic integrals in terms of elementary functions. The method is simple and fast in comparison to the algebraic case of the Risch-Trager-Bronstein algorithm. This method can quickly solve…
We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion…
We study integration in a class of Hilbert spaces of analytic functions defined on the $\mathbb{R}^s$. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve…
In this work we propose two Hermite-type optimization methods, Hermite least squares and Hermite BOBYQA, specialized for the case that some partial derivatives of the objective function are available and others are not. The main objective…
In multicentric representation of piecewise holomorphic functions one combines Lagrange interpolation at roots of a polynomial $p$ with convergent power series of $p$ as the "coefficients" multiplying the Lagrange basis polynomials. When…
Based on the Hilb-type formula and van der Corput-type lemmas, we present optimal asymptotic estimates for the decay of the Laguerre and Hermite coefficients for functions with algebraic and logarithmic singularities, which in turn yield…
We present a new closed form for the interpolating polynomial of the general univariate Hermite interpolation that requires only calculation of polynomial derivatives, instead of derivatives of rational functions. This result is used to…