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View article: Weighted least squares subdivision schemes for noisy data on triangular meshes
Weighted least squares subdivision schemes for noisy data on triangular meshes Open
This paper presents and analyses a new family of linear subdivision schemes to refine noisy data given on triangular meshes. The subdivision rules consist of locally fitting and evaluating a weighted least squares approximating first-degre…
View article: Multivariate compactly supported C∞ functions by subdivision
Multivariate compactly supported C∞ functions by subdivision Open
This paper discusses the generation of multivariate C∞ functions with compact small supports by subdivision schemes. Following the construction of such a univariate function, called Up-function, by a non-stationary scheme based on masks of…
View article: Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics Open
Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, inc…
View article: Multivariate compactly supported $C^\infty$ functions by subdivision
Multivariate compactly supported $C^\infty$ functions by subdivision Open
This paper discusses the generation of multivariate $C^\infty$ functions with compact small supports by subdivision schemes. Following the construction of such a univariate function, called \emph{Up-function}, by a non-stationary scheme ba…
View article: Non-oscillatory butterfly-type interpolation on triangular meshes
Non-oscillatory butterfly-type interpolation on triangular meshes Open
This paper proposes and analyses a non-oscillatory interpolatory subdivision scheme for data on regular triangular grids, a non-linear analogue of the well-known butterfly subdivision scheme. The scheme is obtained, first, by re-interpreti…
View article: Reproduction Capabilities of Penalized Hyperbolic-polynomial Splines
Reproduction Capabilities of Penalized Hyperbolic-polynomial Splines Open
This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-s…
View article: Annihilation operators for exponential spaces in subdivision
Annihilation operators for exponential spaces in subdivision Open
We investigate properties of differential and difference operators annihilating certain finite-dimensional spaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperboli…
View article: Stirling numbers and Gregory coefficients for the factorization of Hermite subdivision operators
Stirling numbers and Gregory coefficients for the factorization of Hermite subdivision operators Open
In this paper we present a factorization framework for Hermite subdivision schemes refining function values and first derivatives, which satisfy a spectral condition of high order. In particular we show that spectral order $d$ allows for $…
View article: Optimal Holder-Zygmund exponent of semi-regular refinable functions
Optimal Holder-Zygmund exponent of semi-regular refinable functions Open
The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular settin…
View article: Convergence and Normal Continuity Analysis of Nonstationary Subdivision Schemes Near Extraordinary Vertices and Faces
Convergence and Normal Continuity Analysis of Nonstationary Subdivision Schemes Near Extraordinary Vertices and Faces Open
Convergence and normal continuity analysis of a bivariate nonstationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically equivalen…
View article: Smoothing exponential-polynomial splines for multiexponential decay data
Smoothing exponential-polynomial splines for multiexponential decay data Open
In many applications, the definition of fitting models that mimic the behaviour of experimental data is a challenging issue. In this paper a data-driven approach to represent (multi)exponential decay data is presented. We propose a fitting…
View article: Convergence analysis of corner cutting algorithms refining points and refining nets of functions
Convergence analysis of corner cutting algorithms refining points and refining nets of functions Open
In this paper we give an elementary proof of the convergence of corner cutting algorithms refining points, in case the corner cutting weights are taken from the rather general class of weights considered by Gregory and Qu (1996). We then u…
View article: An algebraic approach to polynomial reproduction of Hermite subdivision\n schemes
An algebraic approach to polynomial reproduction of Hermite subdivision\n schemes Open
We present an accurate investigation of the algebraic conditions that the\nsymbols of a univariate, binary, Hermite subdivision scheme have to fulfil in\norder to reproduce polynomials. These conditions are sufficient for the scheme\nto sa…
View article: Analysis of level-dependent subdivision schemes near extraordinary vertices and faces
Analysis of level-dependent subdivision schemes near extraordinary vertices and faces Open
Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically equivale…
View article: Convergence and normal continuity analysis of non-stationary subdivision\n schemes near extraordinary vertices and faces
Convergence and normal continuity analysis of non-stationary subdivision\n schemes near extraordinary vertices and faces Open
Convergence and normal continuity analysis of a bivariate non-stationary\n(level-dependent) subdivision scheme for 2-manifold meshes with arbitrary\ntopology is still an open issue. Exploiting ideas from the theory of\nasymptotically equiv…
View article: Convergence and $C^1$-regularity analysis of non-stationary subdivision schemes near extraordinary vertices and faces
Convergence and $C^1$-regularity analysis of non-stationary subdivision schemes near extraordinary vertices and faces Open
Convergence and regularity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically equivalent subd…