Related papers: A Bivariate Polynomial Problem for Matrices
Singular boundary value problems (SBVPs) arise in various fields of Mathematics, Engineering and Physics such as boundary layer theory, gas dynamics, nuclear physics, nonlinear optics, etc. The present monograph is devoted to systems of…
In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are…
Motivated by an application in Magnetic Particle Imaging, we study bivariate Lagrange interpolation at the node points of Lissajous curves. The resulting theory is a generalization of the polynomial interpolation theory developed for a node…
In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear…
A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we…
In this paper, linearly structured partial polynomial inverse eigenvalue problem is considered for the $n\times n$ matrix polynomial of arbitrary degree $k$. Given a set of $m$ eigenpairs ($1 \leqslant m \leqslant kn$), this problem…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vall\'ee Poussin filters. These polynomials can be an useful device for many theoretical and…
The complete eigenstructure, or structural data, of a rational matrix $R(s)$ is comprised by its invariant rational functions, both finite and at infinity, which in turn determine its finite and infinite pole and zero structures,…
We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a…
The bivariate difference filed $(\mathbb{F}(\alpha, \beta), \sigma)$ provides an algebraic framework for a sequence satisfying a recurrence of order two and it could transform the summation involving a sequence satisfying a recurrence of…
We present certain existence criteria and parameterisations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to…
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…
We study the bifurcation values of real polynomial maps $f: \bR^{2n} \to \bR^2$ which reflect the lack of asymptotic regularity at infinity. We formulate real counterparts of some structure results which have been previously proved in case…
The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in $\C^d.$ We study this problem on general sets, but devote special attention to product sets…
This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical…
This is a short note that explains a problem on polynomial maps over finite fields for non-experts. The problem is: Do there exist odd polynomial automorphisms over the finite fields with 4,8,16,32,64,... elements? The explanation is very,…
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,…