Related papers: A unified framework for the computation of polynom…

This paper presents a weighted optimization framework that unifies the binary,multi-valued, continuous, as well as mixture of discrete and continuous treatment, under the unconfounded treatment assignment. With a general loss function, the…

A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over the volume of the ball in three dimensions is described. Such methods are necessary in many areas of Applied…

In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…

The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer.…

This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving…

In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the approximation of ordinary differential equations, is…

An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant…

This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in arXiv:1304.0708 to global function fields of odd characteristics. First, we present algorithm for checking if a given…

We present a polyhedral algorithm to manipulate positive dimensional solution sets. Using facet normals to Newton polytopes as pretropisms, we focus on the first two terms of a Puiseux series expansion. The leading powers of the series are…

Iterating Newton's method symbolically for the general quadratic yields a rational function, the numerator and denominator of which are polynomials with highly composite coefficients.

Counterparts of several classical results of number theory are proven for the ring of polynomials with coefficients in a number field. A theorem of Milnor that determines the Witt ring of a function field is applied to prove an analogue of…

Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…

We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where…

Calabro et al. (2017) changed the paradigm of the mass and stiffness computation from the traditional element-wise assembly to a row-wise concept, showing that the latter one offers integration that may be orders of magnitude faster.…

Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…

Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. The polynomial interpolant is expressed in terms of function values using the so-called barycentric weights, which depend on the…

The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…

We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…

It is shown how to compute quotients efficiently in non-commutative univariate polynomial rings. This extends earlier work where efficient generic quotients were studied with a primary focus on commutative domains. Fast algorithms are given…