Related papers: Scalar Subdivision Schemes and Box Splines
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
The method of constructing spline classes in the form of trigonometric Fourier series whose coefficients have a certain decreasing order are considered. in turn, this decrement determines the number of continuous derivatives of sum of this…
In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of…
Skyline queries are important in many application domains. In this paper, we propose a novel structure Skyline Diagram, which given a set of points, partitions the plane into a set of regions, referred to as skyline polyominos. All query…
Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polynomial that completely determine when the Hilbert scheme is…
We give a general description of the spectral space of conjugacy classes of subgroups of Sp(2): it is a disjoint union of finitely many blocks, each dominated by a subgroup: of these blocks, 26 are of dimension 1, 6 are of dimension 2 and…
Given a graph with edges labeled by elements in $\mathbb{Z}/m\mathbb{Z}$, a generalized spline is a labeling of each vertex by an integer $\mod m$ such that the labels of adjacent vertices agree modulo the label associated to the edge…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
Several properties of stationary subdivision schemes are nowadays well understood. In particular, it is known that the polynomial generation and reproduction capability of a stationary subdivision scheme is strongly connected with sum…
Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical…
We study what we call quasi-spline sheaves over locally Noetherian schemes. This is done with the intention of considering splines from the point of view of moduli theory. In other words, we study the way in which certain objects that arise…
We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces, whose components intersect in a transversal way but may be themselves singular. Such hypersurfaces will be called…
Subword complexes were defined by A.Knutson and E.Miller in 2004 for describing Gr\"obner degenerations of matrix Schubert varieties. The facets of such a complex are indexed by pipe dreams, or, equivalently, by the monomials in the…
The subdivision algorithm by Dellnitz and Hohmann for the computation of invariant sets of dynamical systems decomposes the relevant region of the state space into boxes and analyzes the induced box dynamics. Its convergence is proved in an…
Semialgebraic splines are bivariate splines over meshes whose edges are arcs of algebraic curves. They were first considered by Wang, Chui, and Stiller. We compute the dimension of the space of semialgebraic splines in two extreme cases. If…
An invariant theoretic characterization of subdiscriminants of matrices is given. The structure as a module over the special orthogonal group of the minimal degree non-zero homogeneous component of the vanishing ideal of the variety of real…
We present an accurate investigation of the algebraic conditions that the symbols of a convergent, univariate, binary, non-stationary subdivision scheme should fulfill in order to reproduce spaces of exponential polynomials. A subdivision…
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…
Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD for generating subdivision curves and in computational mathematics for building Hermite…
Employing a matrix mask, a vector subdivision scheme is a fast iterative averaging algorithm to compute refinable vector functions for wavelet methods in numerical PDEs and to produce smooth curves in CAGD. In sharp contrast to the…