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Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
The intention of this note is two-fold. First, we study integer optimization problems in standard form defined by $A \in\mathbb{Z}^{m\times{}n}$ and present an algorithm to solve such problems in polynomial-time provided that both the…
The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…
By a symbolic method, we introduce multivariate Bernoulli and Euler polynomials as powers of polynomials whose coefficients involve multivariate L\'evy processes. Many properties of these polynomials are stated straightforwardly thanks to…
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…
Effective computation of resultants is a central problem in elimination theory and polynomial system solving. Commonly, we compute the resultant as a quotient of determinants of matrices and we say that there exists a determinantal formula…
We present a method to decompose a set of multivariate real polynomials into linear combinations of univariate polynomials in linear forms of the input variables. The method proceeds by collecting the first-order information of the…
Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…
} The main goal of this note is to provide new, mostly multidimensional densities, compactly supported and list many of its properties that enable effective calculations. The idea of obtaining such densities is firstly to build some…
Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
Models which include domain constraints occur in myriad contexts such as econometrics, genomics, and environmetrics, though simulating from constrained distributions can be computationally expensive. In particular, repeated sampling from…
A new polynomial sieve is presented and used to show that almost all integers have at most one representation as a sum of two values of a given polynomial of degree at least 3.