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Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
A new family of combined subdivision schemes with one tension parameter is proposed by the interpolatory and approximating subdivision schemes. The displacement vectors between the points of interpolatory and approximating subdivision…
This article proposes a bivariate polynomial problem for finite-order real matrices that endows a \textit{`sufficient condition'} for a map from the standard vector spaces of finite-order real matrices to the same dimensional bivariate…
We study the computational complexity of decomposing finite discrete dynamical systems (FDDSs) in terms of the semiring operations of alternative and synchronous execution, which is useful for the analysis of discrete phenomena in science…
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
We consider the disjoint bilinear programming problem in which one of the disjoint subsets has the structure of an acute-angled polytope. An optimality criterion for such a problem is formulated and proved, and based on this, a polynomial…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…
High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…
A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying quite mild assumptions. To…
In this work we construct subdivision schemes refining general subsets of R^n and study their applications to the approximation of set-valued functions. Differently from previous works on set-valued approximation, our methods are developed…
Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining B\'{e}zier form of the $L^2$-solution of the problem of best polynomial approximation of B\'{e}zier curve or surface. In this connection, the…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…
In contrast to the univariate case, interpolation with polynomials of a given maximal total degree is not always possible even if the number of interpolation points and the space dimension coincide. Due to that, numerous constructions for…
The notion of multivariate $P$- and $Q$-polynomial association scheme has been introduced recently, generalizing the well-known univariate case. Numerous examples of such association schemes have already been exhibited. In particular, it…