Related papers: Chebyshev Varieties
Given a rational monomial map, we consider the question of finding a toric variety on which it is algebraically stable. We give conditions for when such variety does or does not exist. We also obtain several precise estimates of the degree…
Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses…
We present a common framework to study varieties in great generality from a categorical point of view. The main application of this study is in the setting of algebraic categories, where we introduce Birkhoff varieties which are essentially…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
In this paper we introduce a new family of wavelets, named Chebyshev wavelets, which are derived from conventional first and second kind Chebyshev polynomials. Properties of Chebyshev filter banks are investigated, including orthogonality…
We construct multiple representations relative to different bases of the generalized Tschebyscheff polynomials of second kind. We build the change-of-basis matrices between the generalized Tschebyscheff of the second kind polynomial basis…
We explain in detail the definition, construction and generalisation of the Galois group of Chebyshev polynomials of high degree to the Galois group of chaotic chains. The calculations in this paper are performed for Chebyshev polynomials…
We study certain kind of polynomials associated with Lissajous curves, called Chebyshev-Lissajous polynomials. We investigate their irreducibilities over the real numbers and complex numbers, thus comfirming two conjectures proposed by…
We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms…
We investigate the automorphism groups of the algebraic curves \[ \mathcal{C}_d : y^d = \varphi_d(x), \] where $\varphi_d(x)$ denotes the Chebyshev polynomial of degree $d$, defined over a field $k$ with $p:=\operatorname{char}(k) \nmid…
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs).…
Let t be any integer and fix an odd prime ell. Let Phi(x) = T_ell^n(x)-t denote the n-fold composition of the Chebyshev polynomial of degree ell shifted by t. If this polynomial is irreducible, let K = bbq(theta), where theta is a root of…
We deal with the algebraicity of an iterated Puiseux series in several variables in terms of the properties of its coefficients. Our aim is to generalize to several variables the results from [HM15]. We show that the algebraicity of such a…
In this short note, we give simple proofs of several results and conjectures formulated by Stolarsky and Tran concerning generating functions of some families of Chebyshev-like polynomials.
In this paper, an efficient method is presented for solving three dimensional Volterra integral equations of the second kind with continuous kernel. Shifted Chebyshev polynomial is applied to approximate a solution for these integral…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
In this paper, the dynamics of the Chebyshev-Halley family is studied on quadratic polynomials. A singular set, that we call cat set, appears in the parameter space associated to the family. This cat set has interesting similarities with…
Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…
We propose an algebraic framework generalizing several variants of Prony's method and explaining their relations. This includes Hankel and Toeplitz variants of Prony's method for the decomposition of multivariate exponential sums,…
The purpose of this paper is to give an explicit formula which allows one to compute the dimension of the cohomology groups of the sheaf $\Omega_{\P}^p(D)$ of p-th differential forms of Zariski twisted by an ample invertible sheaf on a…