Related papers: Anisotropic spline approximation with non-uniform …
This paper introduces a class of k-nearest neighbor ($k$-NN) estimators called bipartite plug-in (BPI) estimators for estimating integrals of non-linear functions of a probability density, such as Shannon entropy and R\'enyi entropy. The…
We prove uniform $L^p$ bounds for multilinear operators which are given by multipliers whose symbols are singular on a one dimensional subspace. The novelty is that these bounds are uniform in the choice of the subspace.
In this paper, we study anisotropic Bessel potential and Besov spaces, where the anisotropy measures the extra amount of regularity in certain directions. Some basic properties of these spaces are established along with applications to…
In this paper, we present a nonlinear least-squares fitting algorithm using B-splines with free knots. Since its performance strongly depends on the initial estimation of the free parameters (i.e. the knots), we also propose a fast and…
The purpose of this article is to introduce a new class of kernels on SO(3) for approximation and interpolation, and to estimate the approximation power of the associated spaces. The kernels we consider arise as linear combinations of…
A new class of rational parametrization has been developed and it was used to generate a new family of rational functions B-splines $\displaystyle{{\left({}^{\alpha}{\mathbf B}_{i}^{k} \right)}_{i=0}^{k}}$ which depends on an index $\alpha…
We study a new simple quadrature rule based on integrating a $C^1$ quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions…
Let $\Lambda \subset R$ be a strictly increasing sequence. For $r = 1,2$, we give a simple explicit expression for an equivalent norm on the trace spaces $W_p^r(R)|_\Lambda$, $L_p^r(R)|_\Lambda$ of the non-homogeneous and homogeneous…
In this paper, the asymptotic theory presented in (Caponera et al., 2022) for spline-type anysotropic covariance estimator on the 2-dimensional sphere is generalized to the case of connected and compact two-point homogeneous spaces.
This report studies local asymptotics of P-splines with $p$th degree B-splines and a $m$th order difference penalty. Earlier work with $p$ and $m$ restricted is extended to the general case. Asymptotically, penalized splines are kernel…
This work focuses on the development of a posteriori error estimates for fourth-order, elliptic, partial differential equations. In particular, we propose a novel algorithm to steer an adaptive simulation in the context of Kirchhoff plates…
B-splines of order $k$ can be viewed as a mapping $N$ taking a $(k+1)$-tuple of increasing real numbers $a_0 < \cdots < a_k$ and giving as a result a certain piecewise polynomial function. Looking at this mapping $N$ as a whole, basic…
To predict smooth physical phenomena from observations, spline interpolation provides an interpretable framework by minimizing an energy functional associated with the Laplacian operator. This work proposes a methodology to construct a…
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations…
In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…
We propose to incorporate grain boundary (GB) anisotropy in phase-field modeling by extending the standard partial differential equations formulation to include a nonlocal functional of an orientation field. Regardless of the number of…
We study the interrelation between the limit $L_p(\Omega)$-Sobolev regularity $\overline{s}_p$ of (classes of) functions on bounded Lipschitz domains $\Omega\subseteq\mathbb{R}^d$, $d\geq 2$, and the limit regularity $\overline{\alpha}_p$…
This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These…
P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…